The Studio Theater at the Apollo has a separate entrance from that which leads to Million Dollar Quartet. It is just south of the main entrance, on the lower level, under the lower level marquee on the left in this picture.
There is construction going on as they expand the theater lobby. But that will not impede your access to the downstairs studio.
The Apollo has parking spaces under the el which are $15 if they are available. The street parking is $2.50 per hour and The Submission is done by 9 pm each night.
Parking on Lincoln on Sundays is free. There is also free parking by Jonquil Park on Wrightwood (west of Lincoln) and Sheffield.