Hello, Can you response whether these words exist or not. "Amigxi", "Razigxi" (as he shaves, "Li razis sin").
1. The "amigxi".
As the gramatic rules say:.
"An IĜ verb may also be made from a transitive verb. IĜ there serves to make the verb intransitive.
La knabo malfermis la pordon.
La pordo brue malfermiĝis.
An IĜ verb made from a transitive verb is often similar to a passive verb. The difference is that an IĜ verb shows that the action happens more or less on its own, or that the speaker isn't interested in who or what initiated the action:
Li estis naskita en Januaro.
Li naskiĝis en Januaro. He became born."

Now the question:
Ami - to love.
Amigxi - to be loved.
Oni ekamas min.
They become to love me.
Mi ekamigxas. - I become to be loved.
Does it make any sense?

2."Razigxas". A dictionary says: "se la razilo estas malakra la barbo razigxas malbone", But can I use "razigxas" when I am talking about people?:
He drinks coffee while he shaves.
Li trinkas kafo dum li razis sin.
Li trinkas kafo dum li razigxas.
Which one is preferred (correct)? And What is the difference between them?

Thanks.

Dum serĉo per Kukolo montras ke amiĝi estas uzata, tiu formo mankas en PIV, kaj mi dirus ke la plej kutima formo estas 'enamiĝi al' (to fall in love with, become enamoured of).

To be loved.- esti amata
To become loved - fariĝi amata

Ĉu eble - trinki kafon dum oni razas sin? Ŝajnas risko-plena.

The difference is that an IĜ verb shows that the action happens more or less on its own, or that the speaker isn't interested in who or what initiated the action - Via citaĵo.

Do,
Li trinkas kafon dum li razis sin. He is doing the shaving
Li trinkas kafon dum li raziĝas. He drinks coffee whilst being shaved

sudanglo, I don't want to pick on you specifically here, because I see this happening a LOT on the Lernu! forum across the board by a ton of people, but it kind of bugs me. You've given a good example, though, that I feel serves as a point of illustration.

The OP is clearly a beginner, and he wrote his post in English. Why are you responding in a language he probably doesn't speak very well? And, isn't it safe to assume that if he DID want a response in Esperanto, his question would have been IN Esperanto?

I really wish people would match the languages of the answers to the languages of the questions. This is a board for beginners. Asking a question that you really want an answer to, and receiving a load of hatted-character gobbledy-gook in response is more likely to chase beginners away, because it's straight-up unfriendly. They're beginners. They don't speak the language yet, which is probably why they aren't asking their questions in Esperanto. So answering them in Esperanto isn't, you know, likely to be helpful. "Here, I'll give you an answer IF YOU CAN FIGURE IT OUT HAHAHAHAHA". I get that Esperanto is easier than most languages, but it can still be really impenetrable to a beginner. Don't make them work for it.

I don't mean to say that this even applies strongly in this particular situation, as I don't know the OP or his level of Esperanto. But just as a general rule, it seems to make sense to answer beginners questions in the languages of the questions they asked. I mean, I guess I could be off here, but I just feel like if I were a beginner and I started trying to read the first sentence of your response, I'd be less likely to ask anything further, and not in a good way.

sudanglo:Dum serĉo per Kukolo montras ke amiĝi estas uzata, tiu formo mankas en PIV, kaj mi dirus ke la plej kutima formo estas 'enamiĝi al' (to fall in love with, become enamoured of).

To be loved.- esti amata
To become loved - fariĝi amata

Ĉu eble - trinki kafon dum oni razas sin? Ŝajnas risko-plena.

The difference is that an IĜ verb shows that the action happens more or less on its own, or that the speaker isn't interested in who or what initiated the action - Via citaĵo.

Do,
Li trinkas kafon dum li razis sin. He is doing the shaving
Li trinkas kafon dum li raziĝas. He drinks coffee whilst being shaved

Thank you, but I don't understand what the "searching by Cuckoo" means. I searched the internet and dictionaries, but couldn't find any mention of "amigxi". Now I can't feel free to use the suffixes and preffixes if I don't know whether a word exists. Someone told me that "amigxi" could mean "to become the love". Like
La simpatio inter ili iom post iom amigxis. But I can't accept that because "Ami" have a verb root.
Again, thank you for your time that you spent for me.

Edited 2020-01-29

Espels,

Plena Manlibro de Esperanta Gramatiko (PMEG or nicknamed "Pomego", big apple) is one of the most central contemporary works of the Esperanto grammar. It explains very thoroughly the grammar… in Esperanto. I.e. you must master the language quite a bit in order to understand it. A deeper understanding the grammar of your native language helps a lot.

From PMEG… (my translation and shortening)

The basic meaning of -iĝi is "to become…".
 

• esti → estiĝi : to be → to become into being, to happen

However this "becoming" means a little different things depending on the root. According to PMEG one can classify iĝi verbs to four categories.

Ordinary iĝi verbs

The esti example above falls into this category. The root can also be something else than a verb.
 

• malpura → malpuriĝi : dirty → to become dirty

Iĝi verbs formed from transitive verbs

To shave always requires a direct object in Esperanto, i.e. razi sin. An iĝi verb of such verb has a passive voice character [it is still active voice in Esperanto], "to let becoming…".
 

• razi sin → raziĝi : to shave oneself → to let be shaved ("I had me shaved")

Iĝi verbs formed from intransitive verbs

This category has fallen out of use, but Zamenhof used it to mark unexpectedness, especially as a contrast to something else. In contemporary language you can use other means to express the same idea.

Special cases

There are some verbs, where the meaning of the iĝi form has shifted to mean beginning of an action, i.e. the same as the prefix ek. PMEG even recommends the ek forms.
 

• sciiĝi = ekscii : to get to know
  
• sidiĝi = eksidi : to sit down
  
• timiĝi = ektimi : to be/get scared, frightened

PS. I think that by Kukolo Sudanglo refers to Guglo, Google.

Metsis:Espels,

Plena Manlibro de Esperanta Gramatiko (PMEG or nicknamed "Pomego", big apple) is one of the most central contemporary works of the Esperanto grammar. It explains very thoroughly the grammar… in Esperanto. I.e. you must master the language quite a bit in order to understand it. A deeper understanding the grammar of your native language helps a lot.

From PMEG… (my translation and shortening)

The basic meaning of -iĝi is "to become…".
 

• ami → amiĝi : to love → to become in state of love = to fall in love

However this "becoming" means a little different things depending on the root. According to PMEG one can classify iĝi verbs to four categories.

Ordinary iĝi verbs

The ami example above falls into this category. The root can also be something else than a verb.
 

• malpura → malpuriĝi : dirty → to become dirty

Iĝi verbs formed from transitive verbs

To shave always requires a direct object in Esperanto, i.e. razi sin. An iĝi verb of such verb has a passive voice character [it is still active voice in Esperanto], "to let becoming…".
 

• razi sin → raziĝi : to shave oneself → to let be shaved ("I had me shaved")

Iĝi verbs formed from intransitive verbs

This category has fallen out of use, but Zamenhof used it to mark unexpectedness, especially as a contrast to something else. In contemporary language you can use other means to express the same idea.

Special cases

There are some verbs, where the meaning of the iĝi form has shifted to mean beginning of an action, i.e. the same as the prefix ek. PMEG even recommends the ek forms.
 

• sciiĝi = ekscii : to get to know
  
• sidiĝi = eksidi : to sit down
  
• timiĝi = ektimi : to be/get scared, frightened

PS. I think that by Kukolo Sudanglo refers to Guglo, Google.

Thanks a lot for your response, but I disagree with you. The root "ami" has a prime transitive verbs root meaning. We can find out it by PIV. "Ami' is located on the top of the page. The other meaning (like "amo", "ama" etc) is placed below.
That approves that "amigxi" meaning is "to let become" or "to let be loved".

Vi pravas. I corrected the text.

Metsis:Vi pravas. I corrected the text.

thank you again. But the question about "amigxi" is still open for me.
The main qiestion is not about only "amigxi". Its about all verbs. Can I use suffixies to build a new verb from a random worb or I have to use only common verbs which I totally sure exist? In this
case suffix only help to understand the meaning.
I know the quiestions I asked are the beginners questions, and they will disappear further themselves but now I can't have a peace because of them.

You may use the affixes anywhere that they make sense. There are no word restrictions. For example, in English you can have better, faster, higher, etc., but you can't have gooder, or funner. Weird situations like this do not exist in Esperanto.

You do have to take the meanings of the parts of the words into account, though. It is possible to create words whose meanings are questionable or outright nonsensical because the various bits don't fit together in ways that are clear. But, in Esperanto, there are no exceptions to the rules, and anything can be put together with anything as long as what you are creating is actually clear and meaningful, and not self-contradictory or otherwise puzzling in nature. Just because you can say plikato, and the three pieces (pli\kat\o) are individually comprehensible, doesn't mean plikato is comprehensible (although I can easily think of meanings for plikata and plikate - it's the noun form that's weird).

It might help if you think of Esperanto as not having "verbs", per se, but instead having roots with verbal endings. Some roots lend themselves to being verbs more easily, some lend themselves towards being nouns or adjectives, and so on, but the core of Esperanto is roots, not verbs\nouns\adjectives\adverbs. And anything you can do to one root (modifying them with various types of prefixes and endings, combining them with other roots, etc.), you can do to another root. As long as it makes sense.

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Generally I feel free to edit my posts like a madman UNTIL someone posts something following it. I did edit my post after you made yours, Metsis, but I don't believe I changed the meaning of what I wrote. The shifting sands of my post will solidify now.

It is like RiotNrrd says: in theory yes, you can do, but in practise make sure the word makes sense. Which make sense then, you probably ask next. At least those which you can find in PIV.

Finally a warning. Verbs with iĝi are always in active voice in Esperanto, even if some speakers try to use it in a sort of passive voice, e.g. libro legiĝas is not correct, because a book cannot read itself.