If the target opponent is an illegal target as Cruel Ultimatum tries to resolve, it won't resolve and none of its effects will happen. (I'm not going to list them all here because it would just be disappointing to hear all of the things you won't get to do.)

Cruel Ultimatum's only target is an opponent. You don't choose which creature card in your graveyard you'll return to your hand until Cruel Ultimatum resolves.

All of the actions for Cruel Ultimatum are performed sequentially, in the order listed. Earlier actions may affect how you perform later actions. For example, if the opponent sacrifices a creature that they control but you own, it will end up in your graveyard. When Cruel Ultimatum lets you return a creature card from your graveyard to your hand, you can choose that one.

If, as Cruel Ultimatum begins to resolve, your opponent's life total is 5 or less and you have two or fewer cards in your library, the game will result in a draw. Your opponent's life total will drop to 0 or less, but Cruel Ultimatum must finish resolving completely before state-based actions are performed. You'll then be forced to draw three cards and fail to draw one. When state-based actions are finally performed, you and your opponent will both lose the game at the same time, which means the game is a draw.