It applies to both melee and ranged attacks.
For ranged attacks, the asterisks count as hits.
For melee, it's the number of attacks that go unblocked. For example, if your opponent attacks with Claw and Bite, and you only defend with one Claw, then one hit would go through.
Correct. So if your Battle Dragon is hit once with a ranged attack. He should be turned sideways to indicate that. He then only have 1 hit left for the Melee phase.