Just about any theatre in the English speaking world has seen a Shakespeare play at some time or another. The first theatres to see them were as far as we know The Rose Theatre and Newington Butts Theatre. Other early theatres at which Shakespeare's plays were performed included the Theatre, the Curtain, the first and second Globes, and the Blackfriars. And of course the plays were often performed at venues other than dedicated theatres, such as rooms at court.
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
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).
Actors. Before 1660, only actors and no actresses performed in the plays.
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.