There are absolutely no records of Shakespeare's private life, so if he ever did such a thing, we would have no way of knowing. There is no reason to think he did.
There are no records of William Shakespeare appearing in any productions
Since he was Shakespeare, he thought of Shakespeare as himself.
I think you would have to ask Shakespeare himself that question.
The best one can say about when Shakespeare began his profession is that he had established himself before 1592.
Some Shakespeare wrote himself, others were more or less public domain fold songs.
He didn't. He belonged to a company called The Lord Chamberlain's Men. This is like asking why Mr. Eastman called himself Kodak. He didn't. He called himself Mr. Eastman. Likewise William Shakespeare called himself William Shakespeare. The Lord Chamberlain's Men was a company formed by Richard and Cuthbert Burbage and a number of other actors including Will Kempe and William Shakespeare. They were called that because their aristocratic patron (without whom the company would be illegal) was the Lord Chamberlain.
William Shakespeare spent considerable time and money obtaining a grant of arms for his father. That meant that his father had his own personal coat of arms which William (being the eldest son) would inherit on his death. It also meant that he could call himself "Mr. William Shakespeare" or "William Shakespeare, gent."; without the grant of arms he was plain "William Shakespeare."
The gist of this conspriracy theory is that William Shakespeare did not pen all his plays himself. If or even how this can be proved is doubtful.
He had a company of actors (all male) and there were times when he would perform himself.
The latest published research indicates that both William Shakespeare's parents were Catholic as well as William, himself, howbeit secretly as Queen Elizabeth I was killing off any Catholics she could find.
There is little known of William Shakespeare's marriage, or even Shakespeare himself. What we do know is that after Shakespeare retired from theatrical life in London, he moved back in with his wife in Stratford as if nothing had happened, an event which argues that they were happily married even if often apart.
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