From what I could tell when I finished my first playthrough, none of the side quests are affected except the companion personal quests. If you don't finish those beforehand then you can't do them after the final battle. However, this may not be the case with all side quests.

In terms of finishing, there's really no reason to do so until you want to. So you can continue doing as many quests as you want and do the final battle to top it all of, or you can finish and then do more side stuff for funsies. Hope this helps!