If a permanent enters the battlefield under an opponent’s control with hexproof, indestructible, protection, shroud, and/or ward after Shay Cormac’s first ability resolves, it won’t lose that ability until you activate Shay Cormac’s first ability again. The same is true if an opponent’s permanent gains one of those abilities after Shay Cormac’s first ability resolves.

Because damage remains marked on a creature until damage is removed as the turn ends, damage previously dealt to a creature with indestructible may cause it to be destroyed if Shay Cormac’s first ability resolves later during that turn. This is notably not the case with protection, as protection prevents damage.

Shay Cormac’s second ability resolves before the spell or ability that caused it to trigger. It resolves even if that spell or ability is countered.

Shay Cormac’s last ability looks for any bounty counter on a creature, not just one from that Shay Cormac. For example, if players A and B each control a Shay Cormac and player A has put a bounty counter on player C’s creature, both players A and B will put two +1/+1 counters on their respective Shay Cormacs when that creature dies.