SIDE JOB: Each time Death's Head hits with an attack and actions resolve, you may deal 1 unavoidable damage to another friendly character within 3 squares. If you do, Death's Head may be given one action as a free action but can't attack any character he already attacked this turn.

After, you hit the first character and then hit a the second character, can you hit a third character if possible?

Yes, as long as you don't use a power that you've already used in the same turn. For example, you use Exploit Weakness to hit someone. His special triggers, and you could make a second close combat action and use Exploit again against a different (adjacent)target. If he was based with a third target he could then make a close combat action against that one but couldn't use Exploit since he'd already used it as a free action this turn.

With some outside help(BoS) he could get Running Shot and/or Charge and could also use those as part of his free action chain, as long as he doesn't use the same power more than once.

It says "each time" so yes as long as you can keep making attacks and hits without breaking this rule: "A character may not activate the same game effect twice in one turn with free actions"