Hello Sofia, I have been wanting to respond to your post, but I was hoping someone more knowledgeable than I would do it first. But nobody did, so...
Here I am 
This is the beginning of a Hoca joke, in English it reads: "One day, an unwelcome neighbor whom Hoca did not like, knocked on the door and asked if he could borrow his donkey for a day..."
The similarities between the three texts are obvious, although the Turkish "g" in words like "gün" is a "k" in the other two languages. In the first two you see the word "yahxsi", which I presume is "neighbor."
No, badgrammar "yahxi" must be the equivalent of the Azeri word "yahşi" which means "good, nice" etc. so "yahxi körmeydigen" must be "(yahşi) iyi, güzel görmediği" in Turkish of Turkey. So it, literally, means that Hoca doesn't see his neighbour nicely/ the neighbour does not look nice to Hoca, which means Hoca does not like him.
In the given texts, the word for "neighbour" must be "hoxnisi", "hoxnasi" but they have suffixes so, the Turkish word for neighbour "komşu" must be "hoxna" and "hoxni" without suffixes. With suffixes, they mean "komşusu"
In Turkish it is "komsu". But in Turkish the word "yakin" means "close, near". So a Turkish person would probaby understand "Bir yahxsi".
There is no X in Turkish as in the first two. So I guess the word "Hoxnasi" is related to the "Ho?" which is "welcome". Here again, similar, and I think it would be understood.
As I said above "hoxnasi" must mean "komşusu" not related to "welcome".
What I wonder though, and I cannot answer this question myself, is if it would have been possible to write the sentences differently to highlight their likeness.
In the Uyghurqe and Uzbek versions, there is no semicolon after the "knocks on the door". Rather you see verbs that end with a -up/ip morpheme (ixigini urup/ixigini kakip), while in Turksih it is "kapisini caldi".
I know that in Turkish, when you use this -up/ip morpheme, it is like saying "and then", as in "the neighbor knocked on the door, and then...".
Yes you are right, Azeris speak the same way so when I watch Azeri news I don't understand if the news is over or not because they use this "-ip -ıp" suffixes for the past tense. I always wait for something else but they sudddenly stop. They say something like "Azerbaycan prezidenti gelip" and I say "yes, the president comes and then.....what?????" but they mean the president "came". That's it.
So I assume from this that the Uyghurque and Uzbek are using this same verb form, whereas in the Turkish, the author did not choose to use this phrasing, and put a semi-colon instead. Hope that makes sense.
Anyway, I think that the three are very much alike, and also believe that the translations could be re-written to reinforce that (or even re-written to reinforce their differences...)
Yes...For instance in the text there is this word "ixigini" used for the Turkish "kapısını" but I guess "ixig" is the cognate of the turkish word "eşik" which does not mean "door" but "threshold"
I would love to hear from someone else on the subject though, as I am making assumptions based on a very weak knowledge of just one of those three languages...
