Chevill’s middle ability and last ability look for any bounty counter on your opponents’ permanents, not just one from that Chevill. For example, if players A and B each control a Chevill and player A has put a bounty counter on player C’s creature, player B’s Chevill won’t put a counter on anything and both players will gain 3 life and draw a card when that creature dies.

If the creature or planeswalker with a bounty counter on it ceases to be a creature or planeswalker, Chevill’s last ability will still trigger if that permanent is put into a graveyard from the battlefield.

If Chevill leaves the battlefield at the same time that an opponent’s permanent with a bounty counter on it dies, you gain 3 life and draw a card. If Chevill leaves the battlefield before that permanent dies, Chevill’s last ability won’t be around to trigger.

If your life total is brought to 0 or less at the same time that a creature with a bounty counter on it is dealt lethal damage, you lose the game before the last ability goes on the stack.