Can one put feats like Outsmart and Thwart on The Question? She can use Outwit, but does not possess it.

Yes.

Page 19 of the rulebook: "If a character can use a power or ability via a special power or ability, it can be assigned a feat with that power or ability as a prerequisite, but it must be able to use the power or ability on its own."

How nice :O) Thanx!