I don't believe that you can get a list of all the Facebook IDs of users of a particular application. There doesn't appear to be a possible query for this based on an examination of the FQL tables, probably due to performance and privacy reasons. Generally the presumption is that you maintain a local list of users in your own application, and correlate them to Facebook via their ID, so you would already have all these IDs.
To answer your second question though, yes, that is definitely possible. The Facebook API provides both the users.getStandardInfo and the users.getInfo methods, both of which take user Ids and return information about the user, including the name. users.getInfo
can even be used without a session key to just get the name of the user.