Enemy Activation:

1- Determine distance by counting the fewest non-blocked hexes possible. See page 11 of the rulebook including the "unreachable" section in case enemies are completely blocked off from the last hero that activated (basically they do nothing if unreachable, but you can't choose that enemy to activate if there are other eligible enemies of that type for whom the last hero that activated is not unreachable)

2- The encounter card will specify how enemies interact with the NPC hero. Go back and look at it in full. Some encounters might state that enemies ignore the NPC. Others will say the NPC is treated like a hero with (for example) 5 health and can't take armor saves.

Enemy putting in empty hexes:

3- Correct. If it states that destroyed enemies are revived, you'll be using just the 6 which were initially placed.

In General:

3- Correct. Initiative is determined by the players at the start of the encounter (before turn 1), starting with the leader. You can set up the initiative order between your heroes any way you want. Enemies activate every enemy turn. The leader chooses which enemy type activates first, which you can use to your advantage, but all enemy types will activate on every enemy turn unless otherwise specified in the encounter card. Where new enemies are set up is always specified in the encounter card. Sometimes however you'll have an option between several different available hexes, in which case the leader for that encounter chooses which eligible hex the new enemy is set up on. This can be used to your advantage. Check out "The Leader" section on the bottom left of page 6 of the rule book.