drmambo23
The codex entry for Counterstrike will answer all of your questions. It says that if a creature has a quick action melee attack with the Counterstrike trait is ever the defender of a melee attack, it gets to use that melee attack against it's attacker during the Counterstrike Step. It never mentions having to use your action marker, therefore you don't. It never mentions having to have your action marker active or inactive, therefore it doesn't matter. It also doesn't say that this ability is limited to once per round, so you can use it as often as it is triggered.
Thus, with the Hydra or any other such creature, if he is EVER attacked with a melee attack, you will use his counterstrike against the attacker. If he is attacked with multiple melee attack actions in the same round, you will use his counterstrike against EACH of them. It never matters whether he is active or inactive, and it does not affect his ability to take an action at all. You will still get to use his action however you wish.