Was this the name of the engine facility across the Portland Div. from Tower C? What was its function, especially with BET so close?

You hit it right on the head, it was the East Sommerville Round house. I belive it served as a terminal for the Yard 2/ Mystic wharf switchers. It was still standing (part of it) in the early 90's right by the diamond behind the Hood Plant.

During the days of conventional passenger equipment, engines for yd. 2 trains were turned there after cutting off from their train in the yard.

As for storing Mystic Wharf engines, those engines typically were kept at the Wharf, only going back to the BET when needed to service.