Yes, anyone who uses a bomb is the "bad guy", though the problem isn't political, it's a problem of human nature and the inability of people to prevent warfare.

The Nazis had control of the German government but they weren't the German military. It's the same as Israel. It was long argued that the IDF is the people's army, but that is either no longer the case or never was.

Gaza is not a terrorist state because it isn't a "state". It's a territory which is under Israeli control.