How To Check If A Steam Key Is Activated Or Not

It is not possible at all. You can try to activate on your profile, which will lead you to the link for downloading the game, but it won't inform you if you used it. The only way is when you activate a product key that you used already on your account, then Steam will tell you that this Product key is associated with your own account. But that's it.

If it activates the game when activated, that means that it was unactivated and now activated. If it returns duplicate key, then it has been activated. If it brings up product already owned, the key might or might not be activated. There isn't really a way to check without trying out the key otherwise.