Batter Overrunning First Base: Part II

 
The bases are loaded with two outs. With a 3-0 count, the batter (B1) takes ball-4 for a base-on-balls . An excited B1 sprints to 1st base. as the other three runners stroll to their next base. However, the caffeine-fueled B1 overruns 1st base (in foul territory, with no attempt to go to 2nd base) and is tagged by the 1st baseman off the base BEFORE R3 touches home plate.
 
Two questions:
1. Is B1 out when tagged off the base while overrunning 1st base on a base-on-balls?
2. If B1 is tagged out before R3 touches home plate, since this would be the 3rd out of the inning, does R3's run count?

Call
In NF (and only NF -- 8.2.7), a batter that is awarded first base on a base-on-balls is at risk of being tagged out if he overruns first base. B1 is out in question #1.

For question #2, B1 was awarded first base on the base-on-balls and each of the runners' advance is considered an award. The inning is over on the tag of B1, but R3's run counts on the award.