Does Rip Hunter prevent these from being outwitted?

No, only standard or named powers can be protected.

Special Powers and abilities are not covered.

Does Doom have to declare what character (or power) he is trying to outwit prior to the die roll?

Doesn't look like he has to declare "who" hes outwitting at all. It does look pretty straightforward to me as well but i wanted to be sure....and if nperb guy is having difficulty then somethings up.