Should we translate non-english university names? In my country, several universities are prefixed by "Universidade Federal", which can be translated to "Federal University" (e.g., "Universidade Federal do Rio de Janeiro" to "Federal University of Rio de Janeiro"). When publishing a paper, should we translate this part of the name? 

This is a obscure topic; I have some teachers that use "Federal University" and others that use "Universidade Federal". Once I heard that it is better to keep the original name of the university because it helps to keep its identity. However, even translated, it still is very easy to find. If you Google for both names, they will come up in the first positions of the ranking.

Should we translate or keep unstranslated?
The first thing to do is to check if the university has any recommendations about this. If none exist, then the second aspect is to consider if the university is well known under one or another form of the name. The purpose of providing an affiliation and proper address is for the sake of communication. Before e-mail and Internet, most correspondence went by post so a proper address was very important. Now e-mail is used, which means the affiliation is mostly to identify the author and the author's affiliation. Web sites are usually bilingual so finding the university or department is possible in both English and the native language. Most will probably use the English translation because it makes most sense if the remainder of the paper is in English. A point to make is that if one uses the native language for affiliation etc. then problems will arise for those not familiar with, for example, Cyrillic, Chinese or Japanese. So it seems the best way to communicate affiliation/address is to use English translations that are hopefully officially accepted by the university.