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.

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.

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