Questions and observations:

I'm trying to keep a daily journal looking up words I don't know, making lists of neologism to see if they how neo they are.

My grandmother passed away after a very long illness, so the sadness is not touching on grief; I grieved over her loss a decade ago.

Came across a very handy word, and one that seems to be more respectful than the closest English appoximation:

Sepulti - the care given to the disposal of the remains of the deceased. It's more encompassing than "to bury". (enterigo)

Then I hit a snag.

for "undertaker" I got this very gangly word:

sepultentreprenisto

Is there any reason this can't be shortened to

sepultisto?

or

entombigisto

A banker is a bankisto, not a bankentreprenisto

I checked with the translation of A Christmas Carol and undertaker was translated as cxerkfaristo nearly half the syllables.

Is there a shorter more common word to use?

Another word that I can't find a precise translation for is eulogy.

This is surprising as I would think an address about the life of the recently deceased would be fairly universal.

nothing searching either Reta Vortaro or lernu's came up.

I would have thought omagxa parolado might work, but checking the Esperanto definition of omagxo, it is something different than the common meaning of "homage".

Then the word funeral, also was hard to get a precise meaning.

I think of a funeral as being something separate from the enterigo or entombigo. For me a funeral is where you pay your last respects, eulogies spoken, religious rites are conducted.

Entombigo or enterigo I would think either of the physical act or of a graveside service (perhaps where everyone throws a handful of dirt on the coffin after it had been lowered in the grave (which I've only seen in movies. I think that would horribly traumatic for the bereft family members to do).

Then there are a lot of legal terms, which doesn't surprise me that Esperanto doesn't have precise terms for:

next of kin (rajto de parenceco?)
intestate (sen testamento)
probate (administri la postlasajxon/testamenton?)

I think of a funeral as being something separate from the enterigo or entombigo. For me a funeral is where you pay your last respects, eulogies spoken, religious rites are conducted.

funebraĵoj?

Undertaker - direktoro de funebraĵoj. (funebristo might cover a 'mourner'.)

Perhaps mortisto (mortician)

El la Tekstaro:
15 mar 2003 okazis jarĉefkunveno de la Esperanto-Grupo Nurenbergo en la restoracio Platnersanlage. Post mallonga omaĝo al la mortintaj gesamideanoj la unua prezidantino Anny Hartwig resumis la aktivadon dum la lasta jaro.

Tio ŝajnas al mi iu laŭd-parolo or kar-memora parolo. Eŭlogio may be sufficiently international to come in under rule 15.

Next of kin = plej proksima parenco.

Ĉerko is a coffin, so the "undertaker" from Dickens is really a coffin-maker in Esperanto translation.

This is a case where the translation will depend on what aspect of the job we are talking about.

Sepulti is to prepare a body after death. Embalming, cremation, mummification, these would all be methods of "sepultado". The "undertaker", which is a pretty broad term, is a sepultisto only if they are actually doing these tasks.

If you think of a funeral director, who organizes many of these tasks (acquisition of a coffin, getting someone to do the embalming or cremation, organizing a ceremony), then "sepult-entreprenisto" is not really too bad a word, not much worse than "funeral director", which is the term I'd always use in English. The Merriam-Webster defines undertaker as: a person whose job is to arrange and manage funerals. This arranging and managing funerals doesn't really say to me that the person is doing the embalming etc.

The moral of the story is that you can get far in translations by consulting both an English-English dictionary and also an Esperanto-Esperanto dictionary, to supplement what you are getting from En-Eo/Eo-En dictionaries, because you get a much fuller picture of the meanings of the respective words, and how precisely or imprecisely the definitions map to one another. I used the PIV at vortaro.net for my Esperanto definitions. You need to log in to use it but you can use your lernu account, so you don't need to register again.

Aleksachjo:Questions..

For undertaker I might use funebristo. However, as I'm sure you are discovering, in Esperanto there are often several ways to put the same thing.

Funebro means "mourning" (in all senses) so "the funeral" is vaguely expressed as la funebraĵoj (plural) or more specifically funebra soleno/ceremonio/procesio. This is followed by some form of sepulto, typically entombigo/enterigo or kremacio.

I think mortisto is good for "undertaker" because of its simplicity. Sepultisto is okay as well; the purpose of entreprenisto is to make it clear that you're talking about the manager. The word funebristo might be (mis)understood to mean "(professional) mourner".

The specific word for "eulogy" is panegiro. However laŭda parolado is more readily understood.

The "probate" (document certifying the authenticity of the will) is the aŭtentikigo.

The "executor" is the (testamenta) plenumanto. If the person dies sen testamento, the "administrator" is the administranto.

opalo:The word funebristo might be (mis)understood to mean "(professional) mourner".

There are cultures with professional mourners, but in the West I would use it for "funeral director", which includes the physical infrastructure.