The target creature that gets a bounty counter still has the triggered ability it gains even if Mathas leaves the battlefield.

Creatures that receive a bounty counter other than from Mathas's ability resolving won't gain the triggered ability. Creatures that receive more than one bounty counter as Mathas's ability resolves (most likely due to Doubling Season) won't have the ability multiple times.

If Mathas's ability resolves two separate times targeting the same creature, that creature will have two instances of the triggered ability. Each triggers separately when that creature dies.

The opponents who each draw a card and gain 2 life are the opponents of the player who controlled the creature as it died. This may not be the player who controlled the creature when it received a bounty counter.