All of them. That's why they were able to put out a collected plays volume called the First Folio seven years after Shakespeare died. The King's Men owned the scripts and the right to publish them; Shakespeare did not.
He performed in other plays besides his own, certainly. We know he was in two plays by Ben Jonson, Sejanus and Every Man in His Humour. Also, he was not the only playwright working with the King's Men: Fletcher, Middleton and the young Webster also wrote for them. We know from Henslowe that the Chamberlain's Men performed other plays apart from Shakespeare's and Shakespeare, being a member of the company, played in all of them. But he did not star in them. He was a supporting actor, not a star.
None. Shakespeare was not hired by royalty to write. He was hired by his playing company to write. Even when the king was the patron of the company, he did not involve himself in the running of it. As an actor Shakespeare performed many times before Queen Elizabeth and King James, often in his own plays, but he did not write the plays for these occasions. He wrote them for the public theatres.
Shakespeare was a part owner of the Lord Chamberlain's Men, later known as the King's Men.
Yes.
Shakespeare wrote a number of plays, most of them with the intent that they should be performed by his own theatre company, The Lord Chamberlain's Men, later known as The King's Men. The First Folio lists quite a lot of actors who appeared in his plays from this company. At the top of the list is Shakespeare himself, and next, the star of the company Richard Burbage.
Rumor is Shakespeare did not write his own plays published under his name they say he had help writing them.
He wrote his own plays and sometimes performed in those plays
William Shakespeare acted in his own plays in four theatres: the Theatre, Curtain, Globe and Blackfriars. He may also have appeared in his own plays before 1594 with whatever company he was with, but we do not know which company or which theatre.
Yes, the proof that Shakespeare wrote his plays is as good as that for any of his contemporaries. First of all, we know that the Stratford man was the same person as the member of the King's Men acting company because one of the actors left things to Shakespeare in his will and Shakespeare left things in his will to his fellow actors Burbage, Heminges and Condell. Shakespeare's name appears all over the records of the King's Men, so obviously he was the same man. After Shakespeare became a member of the Lord Chamberlain's Men, his plays were exclusively performed by this company, showing that the author was someone associated with the company. What is more, the plays were consistently attributed to Shakespeare during his lifetime by the numerous publishers that published them, with no recorded protest from Shakespeare, the King's Men or anyone else. (Shakespeare's protest when the publisher Jaggard published Thomas Heywood's poetry as Shakespeare's was duly recorded by Heywood in 1612) Believing that the plays were not written by Shakespeare either involves believing that the entire theatrical community of the time was involved in a massive conspiracy to hide the true authorship of the plays (which is impossible) or that someone else wrote the plays and secretly gave them to Shakespeare to use as his own (which is not only highly unlikely, but is as likely for any other author at any time. How do you know whether or not Stephanie Meyers is secretly fronting for some other author?)
Scholars argue over Shakespeare's first theater company. Queen Elizabeth's Men, Lord Strange's Men, and the Earl of Derby's Men are all possibilities. In 1594, Shakespeare, Burbage, and others founded Lord Hunsdon's Men, which became the Lord Chamberlain's Men soon after.
so he could have a place to perform his own plays the way he wanted to
Most of Shakespeare's plays were arranged into five acts by the editors who eventually published them. (Shakespeare was probably not involved in publishing any of his own plays). There is no evidence that Shakespeare deliberately wrote his plays to have five acts - in fact there is quite a lot of evidence that he didn't.