An ability that triggers when counters are put on a permanent will trigger if that permanent somehow enters the battlefield with those counters.

You draw a card and discard a card all while Benthic Biomancer's triggered ability is resolving. Nothing can happen between the two, and no player may choose to take actions.

You can always activate an ability that will cause a creature to adapt. As that ability resolves, if the creature has a +1/+1 counter on it for any reason, you simply won't put any +1/+1 counters on it.

If a creature somehow loses all of its +1/+1 counters, it can adapt again and get more +1/+1 counters.