Tesak, Segugio Infernale di Judith

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.

Count the number of attacking creatures when Tesak, Judith's Hellhound's last ability resolves, including Tesak itself if it's still on the battlefield, to determine how much mana to add.

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.

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

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.