How many shows/performances take place in the US each year?  This
should include musicals, plays, ice shows, the circus, etc. 
Everything.

Questions like this one and the others you are asking are impossible to answer.

There is no possible way to know EVERY single performance that takes
place in the U.S. Sure, someone can track down how many stage union
performances there are, and perhaps even how many
professional-but-not-union performances there are. But then there are
community theatres, schools, churches, etc., etc. that don't even
advertise.

Kriswrite