You make the choice to have the creature with unleash enter the battlefield with a +1/+1 counter or not as it's entering the battlefield. At that point, it's too late for a player to respond to the creature spell by trying to counter it, for example.

The unleash ability applies no matter where the creature is entering the battlefield from.

A creature with unleash can't block if it has any +1/+1 counter on it, not just one put on it by the unleash ability.

Putting a +1/+1 counter on a creature with unleash that's already blocking won't remove it from combat. It will continue to block.

Chaos Imps will have trample if it has any +1/+1 counter on it, not just the one put on it by the unleash ability.