When my stalwart character dies during chalange which i won with my carrion bird - should I shuffle my deck first and then put stalwart on top of my deck or first player should decide what comes first ?

There are 2 possible scenarios here:

1. You used the Carrion Bird on cards that were in your discard pile: the Stalwart character is moribund while you shuffle the ravens back into your deck, so the Stalwart character ends up on top.
2. You used the Carrion Bird on a card in play (which can be itself). Both cards are moribund at the same time, so this is the problematic scenario. There is precedent for the owner of the cards (you, assuming no control changes) choosing the order in which cards go when they go in the same area (deck, discard pile or dead pile, since it doesn't matter for any of the others), so I'd say you choose, regardless of who the first player is (and if I'm wrong, it'll be the first player who decides).

When multiple cards owned by the same player leave play at the same time, the owner of those cards decides the order in which they hit out-of-play areas in which the order matters, like the dead pile, discard pile, deck, etc.

When multiple cards owned by the same player leave play at the same time, the owner of those cards decides the order in which they hit out-of-play areas in which the order matters, like the dead pile, discard pile, deck, etc.

Thanks for reply

This should be written in next FAQ