are agpl3 and gpl3 compatible and can (a)gpl3 use mit / bsd / apache code but mit / bsd / apache cant use (a)gpl3 code?

Generally speaking, you can't. You can license the whole thing AGPL which is fine; if for some crazy reason you don't want to do that you pretty much have to rewrite anything AGPL in order to license the whole thing GPL3. Why would you do that though?