Mills Gallery at the Boston Center for the Arts

Yes, very limited

Loews is probably the nicest, closest, but there are lots of choices nearby.

You can see all performance times, and availability at https://www.huntingtontheatre.org/season/calendar/?date=12-01-2018

They are two stages in the Calderwood with two different capacities - the Virginia Wimberly Theatre and the Nancy and Edward Roberts Studio Theatre. The Wimberly is a 370 seat theatre. The Nancy and Edward Roberts Studio Theatre is a 250 seat theatre.

Back Bay station is closest to the Calderwood Pavilion.

Depends on which theater, on their website it lists capacity for each one

The is limited metered street parking and nearby paid lots and garage. No parking at the theater. The theater is home to a number of theater companies; most use assigned seats but check on each production.

Call the location too ask them directly

I would imagine you can go onto their web site, and contact them. They have a marketing department that can answer your questions.