To add to ZL's excellent answer, the definition of 從子 is complicated and has also undergone changes across history, and that I believe may have been the reason for the varying translations.
In a Song dynasty Confucian collection, 從子 is defined as a way of calling one's nephews. ("兄弟之子當稱從子", Child of brothers [~Nephews/Niece], should be called 從子). That corresponds to the Nephew interpretation.
However, the same book also cited another definition:
"自曾祖而下三代稱從子", from the great grandparents down three generations called 從子. In other words, as long as they share common great-grandparents, 2 people in the family are 從子s. This also means that the brothers of one's father (i.e 從父), if they have children, would also be 從子 to me. Hence the paternal uncle's son interpretation.
And then, there is another interpretation: for person A and B who shared the same great-grandparents, they are known as 從祖兄弟 (literally, cousins related by grandfathers being bothers), Person A's son would be Person B's 從祖兄弟之子(Son of 從祖兄弟), which can be shortened to 從子. And that we have the Xun You case by ZL.
So actually, all of them may be valid! Whichever is the correct interpretation will depend on the specific context and details. As seen in the Xun You and Xun Yu case, we are able to deduce the correct meaning with additional details.
2.The second question is about reading of the names. Some signs have multiple sounds for the same writing.
For example:
For '劉禪', we can have 'Liu Chan' or 'Liu Shan'.
For '全緝', it's 'Quan Ji' or 'Quan Qi'.
For '句安', 'Gou An' or 'Ju An'.
My question is: In each case, which one is the good one ? How is it chosen ? Is there some sort of convention that says one is prefered to the other ? Or is it a free choice of the translator we can read ?
As elaborated by Qin Feng, some characters have different pronunciations (In modern Mandarin, we don't know for sure how they sound like exactly in the past, but there are many reconstructions) depending on the context, and sometimes the distinguishing context is one of family name, such as 句, and that is how we know the pronunciation.
For others that do not have such distinguishing factors, then it's a little more ambiguous. Sometimes we can use their names and courtesy names to make an educated guess, and other times we just have no direct clue at all. There are of course debates to be made (sometimes for both sides), but when we don't have a definite answer often we are just going by convention / dominant arguments here. So for example in the case of 刘禅, it is more often said with 'Shan'.
For Liu Shan, I know 'Shan' means 'abdicate', so maybe is it currently favored by a certain sense of humor, no ?
To elaborate more on why it is 'Shan' , the most convincing argument came from SGZ itself, where someone was recorded to have commented on Liu Shan's name: "后主讳禅，其训授也" The latter lord's name is 禅, meaning to give. The pronunciation for 禅 in modern Mandarin that has the meaning of 'giving up something' is 'Shan', and therefore we generally go by that.
3. Like in my second question, the same name gives different sounds. It could be said so even about ancient places.
(會稽) is 'Kuaiji', 'Huiji' or 'Guiji' ? Which is the good one ?
(琅邪) should be literally 'Langxie', but I found 'Langye' or even 'Langya' ? Is it some sort of transformation of that name by the time passing by ??
This is similar to the second question, with additional complications. People's names only last so long, but location names can last very long, and sometimes they can have character changes or pronunciation changes due to a variety of reasons. To go into the exact process of finding out pronunciations and their evolutions is pretty much also crossing into linguistic realms rather than just history itself, and there are proper academia discussions on them sometimes, but I don't think they are that important for just historical discussions.
For famous location names, the good thing is that conventions are usually recorded in dictionaries/official documentations, so we just have to refer to them for pronunciations. The downside is that Chinese is not only spoken in one country, and also authors/publishers don't necessarily agree, so sometimes the sources may have differing conventions. I have, for example, seen a dictionary giving 'Kuaiji' and another giving 'Guiji'. Though from my limited understanding of linguistics, these 2 pronunciations are of the same root that has undergone different changes in different regional dialects (modern Mandarin largely influced by Beijing dialect).
For 琅邪 though, there is another problem of 通假, another whole can of worms. A quick summary would just be that some characters are used interchangeably for convenience or some other reasons, and the actual character for 邪 is 琊. There are of course still some contention on 'ya' or 'ye', but 'xie' is most certainly not the accepted pronunciation anywhere.
A quick trick is that for location names, if we see different pronunciations rather than the standard pronunciations for that character, they are most likely the correct ones. Historical location names usually have some long histories back when pronunciations and usage were quite different, and them being proper nouns may cause these past relics to be retained, hence leading to a seemingly non-standard pronunciation by today's modern Mandarin standards.
