When the moribund cards physically leave play, they leave all at once or first player chooses the order?

Thanks

All moribund cards leave play at the same time, at the end of each action window. There are no conflicting passive effects for the first player to put in order.

If multiple moribund cards are being put into the discard or dead pile at the same time, the player who owns those cards determines the physical order of the cards.

So, a Brighwater Man-at-Arms stolen with Melisandre's Favor not physically returns to its owner...

Thanks

So, a Brighwater Man-at-Arms stolen with Melisandre's Favor not physically returns to its owner...

I'm not entirely sure what you mean by "not physically returns to its owner"? By the rules, when cards leave play, they always go to their owner's out-of-play area, no matter who controlled them when they left play. So the Man-at-Arms will go to its owner's discard pile at the end of Dominance, no matter who controlled it during the phase. Mel's Favor will also go to its owner's discard pile - a different pile, of course - at the end of Dominance.

Just to say it again, if Player A puts Mel's Favor on Player B's Man-at-Arms, then at the end of the Dominance phase, both the attachment and the character are discarded at the same time (due to their respective text abilities). Player A puts the attachment in his discard pile while, at the same time, Player B puts the character in his discard pile. At the beginning of the Standing phase, both cards are no longer in play and physically in the discard piles of their respective owners.