Can your character be affected by mind control? This is kind of a toughie! Doom was immune from the Purple Man because, well basically he's a badass and can't be tamed (his willpower was too great). However, he was present in the House of M, thus implying that really world-breaking skills could do it? I'm open to the possibility, but it should probably be extremely difficult for him.
Is there anything he just CAN'T make them do? No, Doom is pretty ruthless. It's the end result, not the means to it.
Are you open to him pushing your character's mind? Yes.
If so, in what ways would they be most vulnerable to manipulation? Anything pertaining to self-doubt, particularly in regards to him being in the right/not really a villain.
Are you open to him erasing/implanting memories (if so, what kind?)? Yes, but again it would be difficult and I'm not entirely sure exactly what?
Is there anything you don't want him pushing for/mentioning ever? Nope. Everything is fair game.
Are you open to him pushing other characters for information on your character? Yes.