Arbitrator who will hear Grievance in bounty case gets fired by the MLB

That's a good question, and one I hadn't considered. My understanding is that he is an arbitrator agreed to by both the NFL and the NFLPA, but I might be wrong.

Yes, that's correct. The selection of the arbitrator is not unilateral by the league.

I think he was the one who reversed the Braun suspension (50 games).