When two or more cards are killed/discarded at exactly the same time, in which order do they go to discard/dead piles? In the order their owner wants, or the order the first player says? This is important for Regroup for example.

If a card would be removed from play by two different effects at exactly the same time, the First Player decides which effect goes first (and, therefore, where it ends up).

Sorry for my bad wording. What I meant is, if for example I reveal Valar Morghulis, in what order do my characters go to the dead pile?

Cards removed from play at the same time (or in the same action window, for that matter) go to their respective out-of-play areas in the order chosen by their owners.