Hezbollah is not the Lebanese military. They are a paramilitary gang, comparable to the cartels in Mexico, that gained too much strength for the actual Lebanese military to deal with. Mostly because Iran trained fighters and sent weapons.

Actually a better example than the cartels might be the CIA sponsored paramilitaries in South America. Except Hezbollah is sponsored by Iran obviously.

Yes. But my sense is that the line between Hezbollah's activities and normal government functions is much blurrier in Lebanon.