You can say "I hope I can make friends with you". "make friends with" works if "you" is singular or plural. It could, however, mean "make friends (with other people while I am) with you". I would just say "I hope we can be friends" and not use "make friends" when talking directly to that person / those people.

No, you wouldn't use it in that case. You would say "I hope I can be your friend" or "I hope we can be friends" instead. You can't make a friend WITH someone. Hope this helps :]