1. Constantine
2. It’s a bit harder to say. Doom has fear where he was able to obtain huge power but as his role is a villain, he always ends up losing it. You can’t credit his conquest without admitting he failed to maintain it. Constantine on the other hand never seemed to have the urge to use powerful magic or obtain power. Magic in DCU is more destructive to the user. It’s hard to say what would happen if he actually had the urge/drive to obtain power like Doom does. He has certainly defeat opponents with little required prep.
I personally give the edge to Constantine on scenario 2
Remember when Constantine tricked three hell lords into curing his cancer, because he bargained his soul to all of them? So they reasoned to avoid a war, they'd better keep him in perfect health and make sure he never dies?
If Doom was there, he would have asked the idiots why he had to be healthy and in one piece.
Doom outsmarts the people who outsmarts dumb cosmic beings.