I was thinking about a translation of a book that is in the public domain. The author is Adam Smith. There is already a French translation of some of his works. Does this mean that I cannot publish my own French translation? Does the existence of a French translation preclude the creation of another? Do I have to use a language that it isn't translated into?
Can you think of other cases where there are multiple translation of the same book into the same language? If you search Amazon for classics in one language, do you find multiple translations into other languages? (Try the Divine Comedy or Beowulf or the Iliad -- or the Bible.) What do you find?
Public domain books are no longer under copyright protection and can be used by the public as they wish without fear of copyright infringement. There are classical books that have multiple translations to the same language. However, before starting such a project, I would suggest that you ensure that your translation would be an improvement in some way from the original translation.
Yes, you can.
As stated by others, public domain works - by definition - don't pose limits to uses and reuses. As long as you don't use other translations' solutions or passages (i.e. you don't copy other translations, which would infringe the copyright of the translation, but not of the original work) you're fine.