OBSTAKLO - obstacle

Tio, kio malhelpas aŭ malfruigas la iradon - that which hinders or delays the movement (lit. 'the going').

(propre aŭ figure) - 'figure' certainly means 'figuratively', similar to 'metafore' (metaphorically). The context seems to suggest that 'propre' would mean 'literally' here, but I'm not very familiar with this usage of 'propre'. I've come across 'efektive aux figure' in PMEG.

Esperanto estas taŭga ilo por forigi lingvajn obstaklojn en la komunikado inter la popoloj - Esperanto is a suitable tool for doing away with language barriers (lit. obstacles) in the communication between people.
Ili metis obstaklojn sur nian vojon - They placed obstacles in our way.
Li gajnis la konkurson pri rapideco kaj lerteco en obstakla kurejo - He won the competition about speed and skill in the obstacle course.
Vi obstaklas la lumon al mi! - You're obstructing/blocking the light from me!

MIENO - [facial] expression

1. Esprima aspekto de la vizaĝo kaj de la sinteno - the expressive appearance of the face and of [a person's] attitude.

Laŭ la mieno de la patro mi komprenis, ke pli bone mi lin ne ĝenu - By my father's expression I realised (lit. understood), that I had better not bother him.

Vulpo mienon ŝanĝas, sed plue kokidojn manĝas - The fox changes it's expression, but continues to eat chicks.

Ili faras la mienon kvazaŭ ili laboras - He pretends to work/ He is pretending to work (lit. "He makes the [facial] expression as if he is working"). Or you could say 'Li sxajnigas, ke li laboras'

Ŝi kokete mienas - She is making/makes a flirtatious/coquettish expression
Dum la prelego de tiu gravmiena profesoro ni nur silentis - During the lecture of that grave-faced professor we just remained silent.
La pavoj gravmiene promenadis - The peacocks strolled along solemnly.
La rigidmiena sekretario malĝentile diris, ke ni devas atendi - The stone-faced secretary told us rudely that we had to wait.

2. Karakteriza aspekto de la vizaĝo en difinita malsano - Characterising appearance of the face in a specific illness.

La sana mieno de la avo montris, ke li sentas sin bone - The healthy expression of the grandfather showed that he is feeling better.
Li mienas kiel malsanulo - He's making the expression of an ill person.

HEJTI - to heat (a house, room, a stove etc)

1. Estigi varmigan fajron aŭ elektran ardon en tiucela aparato - To make (lit. 'to bring into being') a warming fire or electric (electrically-produced) heat in a purposely-designed device.

Miaj geavoj loĝas en la vilaĝo kaj vintre devas hejti la fornon - My grandparents live in the village and in the winter they have to fire up/heat up the stove. (this is refering to those big oven/stoves made of stone that houses had in the old days. Maybe there's a better word for it!?)
Vivi inter forno hejtita kaj tablo kovrita - To live between a heated stove and a covered table.
Ni uzas lignon kiel hejtaĵon - We use wood as a fuel for heating. (another word for 'fuel' is 'brulajxo', lit. a thing for burning)
Unue necesas antaŭhejti la miksaĵon - Firstly it's necessary to pre-heat the mixture.

2. Varmigi per speciala aparato - to warm/heat with a special device.

La vetero ekstere iĝis malvarma kaj pro tio oni jam komencis hejti la apartamentojn - The weather outside has become cold and so (lit. 'because of this') they have already begun heating the flats.
Ni devas multe pagi por la hejtado de nia domo - We have to pay a lot for the heating of our home.
Ili hejtas sian apartamenton per gasa hejtilo - They heat their flat with a gas heater.
Ni ne surmetas la puloverojn, ĉar oni superhejtas la ĉambron - We didn't put our jumpers/sweaters/pullovers on because the room is heated (they heat the room). - It would seem fine to simply write 'cxar oni hejtas la cxambron'. I'm not exactly sure what significance, if there is any at all, the addition of 'super' has to the verb (maybe the heating comes from above?! Or perhaps it merely points to the fact that there's a general heating system which covers all the rooms, rather than there being a heating device for just the one room...)

"Central heating" would be 'centra hejtado'.

DISTRI - to distract, to entertain

1. Malhelpe deturni la menson de ĝia okupiĝo - to turn [a person's] mind away from its [current] occupation. 'Malhelpe' means something like 'in a hindering way', sorry can't quite think of the word at the moment!)

La muziko tro distras min kaj mi ne povas lerni - The music is distracting me too much and I can't learn. (It's handy to note the use of 'tro' here. I used to always write things like 'tro multe' for this, translating it straight from the English! It's much easier to simply say 'tro'!)

Li estas tre distriĝema - He's very easily distracted. ('-em-' literally means that the person 'has this tendency/inclination')

(ne kapabla fiksi sian atenton) - not capable of fixing his attention.

2. Deturni la menson de ĝiaj prizorgoj, agrable okupante, amuzante ĝin - To turn [a person's] mind away from its worries [by] pleasantly occupying it, amusing it.

Mi provis ĉiamaniere distri ŝin, ĉar ŝi estis tre malgaja - I tried in every way to distract her because she was very unhappy.

Tiun libron oni povas legi por aventuro kaj distro sen pensi pri aliaj aferoj - One can read that book for adventure (excitement) and distraction without thinking about other things.

Tiam nia vivo estis distra kaj plezura - [Back] then our lives were entertaining/fun and pleasurable. (Here, I mean interesting, varied and not boring when I say 'entertaining/fun')

Lernante Esperanton ni ofte distriĝis - When learning Esperanto we often had a lot of fun (or this could mean 'we were often distracted', depending on the context...)
Dancado estas aktiva distraĵo - Dancing is an active form of recreation.
Tiu loko famas pro distriĝo kaj turismo - That place is famous for entertainment and tourism.

KONVERSACIO - A conversation.

Familiara, ordinare nur distra interparolado - a familiar, usually only entertaining/enjoyable/relaxed exchange.

- sorry about the dodgy translation of 'distra'! It's probably a combination of all those words...
- I suppose 'interparolado' refers to all types of spoken exchanges. So, an interparolado could be a 'konversacio' or a 'diskuto' (discussion) etc...

Mi jam komencis bedaŭri, ke mi enmiksis min en tiun konversacion - I began to regret that I had involved myself (lit. 'mixed myself in') in that conversation.

- Where did 'jam' go?! Well, I ignored it as I can't think of the precise English word for it in this context, if there is one at all! I would say that the purpose of 'jam' here is to simply emphasise the word 'komencis'...

Eble ni ŝanĝu la temon de la konversacio? - Maybe we should change the topic of the conversation?
Ni invitas ĉiujn al nia konversacia rondo! - We invite everyone to our conversation group (lit. rondo=circle)
La virinoj konversaciis pri la kosmetikaĵoj kaj similaj aferoj - The women were talking about (having a conversation about) the cosmetics and [other] similar things.
Li estis interesa konversacianto - He was an interesting conversationalist.

GLATA - smooth

1. Prezentanta nenian elstaraĵon sur sia supraĵo; tia, ke la mano facile glitas - presenting no protrusions on its surface; such, that the hand easily slides [over it]

La haŭto de mia bebo estas tre glata - The skin of my baby is very smooth.
La akvo de la lago estis glata kiel spegulo - The water of the lake was flat like a mirror.
Ŝi glatigas siajn harojn - She flattened, smoothed down her hair (Here, the word 'glatigi' probably has pretty much the same meaning as 'ordigi', as in 'put into order', or 'to straighten out').

Glata, plata or ebena?!

I tend to remember these three words as having the following meanings:
glata = smooth
plata = flat
ebena = level, even

But, as the examples above show, in Esperanto they are sometimes used in slightly different ways to the English words... (For example, I'm not sure I'd say that the water was 'smooth' like a mirror - 'flat' seems the better word - it seems that in Esperanto, glata is used here to emphasize that the water is 'really flat')

2. Senobstrukca, facile irebla - not obstructing, easily passable (lit. easily 'goable'!)

Ni iris laŭ glata vojo - We went along a smooth road

Ĝi estas inter la glataĵoj de la valo - Ok, out of context, this is difficult to understand... 'Glatajxo' litterally means 'smooth thing/area'. Perhaps it is supposed to mean the same as 'ebenajxo' or 'platajxo' (plain) or 'altebenajxo'/'altplatajxo' (plateau)?! Or maybe it really does mean 'the flat/smooth areas of the valley'?! And as I'm not sure about 'glatajxo', it's also difficult to understand whether 'inter' means 'between' or 'among' - the context would make this clear...

3. Iranta sen baro aŭ malhelpo - Going without a barrier or hindrance.

La afero estas sufiĉe glata - The matter is straightforward enough.
Vivi sate kaj glate - To live contentedly and easily (lit. smoothly)
Mi tre esperas, ke ĉio pasos glate - I really hope that everything goes smoothly

Finita kaj glatigita (bone aranĝita) - Finished and smoothed off (well arranged/organised) - ok, this sounds weird! I can't think of the equivalent English phrase at the moment!

Nia konversacio estis malglata - Our conversation didn't go smoothly.

4. Karesa, dolĉa, lerte flata - caressing/kind, sweet, skillfully flattering

Liaj glataj paroloj logis ĉiujn knabinojn - His flattering words lured all the girls.
Infano glatumas la hundon (karese tuŝetas) - The child is stroking the dog (touching gently and caressingly). This is the first time I've seen 'glatumi', but you can kind of guess the meaning. I think it's more usual to say 'karesi la hundon'...

I feel sorry to interrupt, but I absolutely LOVE your commentary! Awesome Job!

GLADI - to iron (clothes).

Glatigi per varmega ilo, ĝin premŝovante tien kaj reen (sur tukoj, vestoj kaj simile) - to smooth [something] with a hot implement, pushing it with pressure backwards and forwards (on cloths, clothes and similar [things])

Patrino nun gladas la vestojn - Mother is now ironing the clothes.
Pantalono jam estas gladita kaj vi povas surmeti ĝin - The trousers have already been ironed and you can put them on.

Note: 'pantolono' is always in the singular for 'trousers'! It's tempting to say 'pantolonoj', but I suppose that would mean 'the pairS of trousers'.

Ne gladu vestojn sur la tablo - ja por tio estas uzata gladotabulo! = Don't iron clothes on the table - an ironing board is used for that! ('ja' just adds emphasis here)
Ĉi tiu pulovero estas negladenda (tia, ke oni ne bezonas ĝin gladi). - This is a non-iron jumper/pullover (such that you don't need to iron it).

"Negladenda" contains the suffix '-end-' which means "devas esti farata" (has to be done), so this word literally translates as 'doesn't have to be ironed'.

Gardu vin! La gladilo estas tre varma! - Be careful! The iron is very hot!

Varma?! Yes, if you look in the Lernu dictionary it will translate this as 'warm'. So you would imagine that 'hot' would be 'varmega' - and this is true, but it seems that some Esperantists have got into the habit of using 'varma' to mean 'hot'... I think I'd rather stick to the distinction between 'varma' and 'varmega', but I suppose if someone does use 'varma' to mean hot, then you can understand it in the context...

ReVo gives a good example, which uses 'varmega' rather than just 'varma':
"Tuj post la hejto la forno estis varmega, post unu horo ĝi estis jam nur varma, post du horoj ĝi estis nur iom varmeta, kaj post tri horoj ĝi estis jam tute malvarma" - Immediately after heating the stove was hot, after one hour it was just warm, after two hours it was only slightly warm (lukewarm), and after three hours it was completely cold.

Mia fratino laboras kiel gladistino en la kudrejo - My sister works as an ironer in the sewing shop.

ESTIMI - to esteem (to regard/rate something/someone highly. To hold someone/something in high esteem)

Note: I think it's worth comparing 'estimi' with 'respekti'. This is made trickier due to the fact that in modern English 'to esteem' is not often used in the verb form! We tend to use other constructions now (as mentioned in the brackets above!)

ReVo gives these definitions:

Estimi - alte taksi ies moralan aux spiritan valoron - to rate highly (or highly regard) someone's moral or spiritual value.

respekto - sento de estimo kaj submetigxo, kiun oni havas antaux iu rangsuperulo aux antaux ia supereco - a feeling of esteem and submission (deference), which one has towards a superior or towards some kind of superiority.

And so,

respekti = Havi senton de respekto al iu aŭ io - to have the feeling of respect towards someone or something.
or "Montri per siaj agoj, ke oni respektas iun aux ion" - to show by one's actions that one respects someone or something.

Here's a good example of the two words in use within one sentence (taken from "Homoj sur la tero"):

"Oni povus facile kredi, ke la homoj rigardis Kristoforon kiel sensenculon, almenaŭ ĝis certa grado. Tiel tamen ne estis. Plej vere, oni estimis lin kaj rigardis lin kun certa respekto" - One could easily believe that the people regarded Kristoforo as a nonsensical person, at least to a certain degree. However it was not so. In actual fact, they held him in high regard (he was highly esteemed/admired by them) and they regarded him with a certain respect.

Back to the Lernu definitions:

Havi altan opinion pri ies morala kaj spirita valoro, aŭ pri ties faroj - to have a high opinion about someone's moral and spiritual value, or about the person's actions.

Ni ĉiuj devas estimi niajn gepatrojn - We must all esteem our parents (hold them in high esteem). You can see here where the possible overlap with 'respect' can be! This sentence is very close in meaning to 'Ni cxiuj devas respekti niajn gepatrojn' - we must all respect our parents.

Estimataj sinjoroj kaj sinjorinoj, estas plezuro vidi vin ĉiujn ĉi tie! - Esteemed ladies and gentlemen, it is a pleasure to see you all here!

Ŝi perdis la estimon por si mem (memestimon) - She lost her self-esteem (The word 'self-esteem would seem to have a slightly different meaning to 'self-respect' or 'memrespekto', which can also suggest that one is behaving with honour and dignity).

Tiu homo estas estiminda, ĉar li faris multon por nia lando! That man is worth of esteem because he has done a lot for our country.
Mi malestimas perfidulojn - I disdain/despise traitors.
Malriĉeco ne estas krimo, tamen kondukas al malestimo - Poverty is not a crime, although it leads to disdain.
Li estas malestiminda mensogulo! - He's a despicable liar.

NUANCO - nuance, shade (of colour)

1. Delikata, apenaŭ sentebla diferenco inter gradoj kaj kombinoj de iu koloro - A slight, barely detectable (lit. feelable!) difference between the grades and combinations of a colour.

Antaŭ farbado de la ĉambro ni elektis inter la diversaj nuancoj de ruĝo - Before painting the room, we chose between various shades of red.
Hela nuanco plivigligos la ĉambron - A bright shade will liven up the room.
Ĉu vi povas instrui al mi la arton nuanci la farbojn? Can you teach me the art of making different shades of colour (I'm not sure about the official term for this, maybe 'shading', 'tinting' or 'toning'...)
La ĉielo nuanciĝis de mil diversaj koloroj - The sky changed to shades of a thousand different colours.

2. Delikata diferenco inter samspecaj aferoj - A slight difference between things of the same type.

Li respondis al mi kun nuanco de malestimo - He replied to me with a hint of disdain.
Esperanto povas esprimi ĉiujn nuancojn de la penso - Esperanto can express all the nuances of [our] thinking.
Raporti pri ĉiuj cirkonstancoj kaj nuancoj - To report about all the circumstances and nuances.