Each time the first ability resolves, a delayed triggered ability is created. Whenever a card is put into an opponent’s graveyard that turn, each of those abilities will trigger. For example, if you activate the first ability twice (and let those abilities resolve) and then activate the second ability targeting an opponent, that player will lose a total of 4 life. Each card put into that player’s graveyard will cause two abilities to trigger, each causing that player to lose 1 life.

The delayed triggered ability created won’t trigger if a token permanent is put into an opponent’s graveyard.

The first ability considers each of your opponents. You don’t choose just one of them.