Most theatres that are not specifically dedicated to one kind of entertainment will, sooner or later, find themselves home to a play by Shakespeare. That is because Shakespeare's plays are so popular that most acting companies want to put them on, and most actors want to play in them.
Assuming you meant professions, Shakespeare was an actor, a poet and a playwright. He also owned shares in the acting company in which he performed and which put on his plays, and in the two theaters in which the company performed.
William Shakespeare's plays were performed in 'The Globe Theatre'.
The Globe Theater
Actors. Before 1660, only actors and no actresses performed in the plays.
Prior to building the Globe, Shakespeare had plays performed at a number of venues: The Theatre, The Curtain, The Swan, and possibly some of the Inn-yard Playhouses. Toward the end of his career, his plays were also performed at Blackfriars private playhouse. There are also records of performances in palaces, and in Grey's Inn (an inn of court).
the global theater
The Globe Theatre.
Newington Butts Theatre
The Globe Theatre
With the exception of the period between 1640 and 1660 or so, Shakespeare's plays have been continuously performed in London since about 1590 or so.
No. We know of at least one, Sir Thomas More, that he and his collaborators could not get past the censors.
Hamlet is the most performed play. As far as I know, none have been prefoomed.