In example a if F2 catches the ball then the batter standing in the box isn't interference. If in the same case he steps back or does something obvious then he is out and the runner returns. All this assumes the out wasn't made at the base.

If the ball wasn't fielded cleanly then the batter is required to clear whatever space F2 needs to make a play. In either situation the batter is out and the runner returns.

In example b the batter is out, no run. If less than two outs the runner would be out which wasn't the case here.