If Belichick does retire who gets the job though, McDaniels or Patricia....or does someone like Saban come back to the NFL and take over that franchise as he and BB are friends and BB can probably forge that hire with Kraft and Saban.
I don't see BB chasing Shula's record, nobody cares about the amount of wins a head coach has in reality. It's about how many rings are on your fingers. BB could have 5 in a couple weeks (as a head coach, more if you count his as an assistant) and I don't think he has some 7 or 8 or 9 year plan to catch Shula as it seems pointless to chase that at his age.
To your first question.....whoever BB suggests to Kraft in his exit interview. But either Josh or Matt.
Yeah I don't see him staying on to chase Shula's record. I see him staying on to prove he can win a Super Bowl without Tom Brady.