Shakespeare was well-respected as an author in his lifetime. There were, of course, other well-respected authors at the time, lots of them.
Some people think that others wrote Shakespeare's plays such as Francis Bacon.
Reasonably so. He died quite well off, and was respected as a playwright at least by others in the theatre community.
The USA did not exist as such during Shakespeare's lifetime so there was no president of the USA. England/UK has never had a president, and during Shakespeare's lifetime there was no such position as prime minister.
I don't think the question is correct. I've always read that though individual editions of some plays were published during Shakespeare's lifetime, he didn't have them published. His acting company may have sold some scripts, and others may have been pirated.
The moon
No, Shakespeare's work was not first published at his baptism. Shakespeare's plays and poetry were published during his lifetime, with the first collection of his plays published in 1623, seven years after his death. However, it is unclear if Shakespeare himself oversaw the publication of his work, or if they were published by others after his death.
Shakespeare was reasonably well appreciated during his lifetime. Nobody thought he was a nutter. He actually led a fairly dull and conventional life.
jumping of walls
There was a lot of play.
The two monarchs on the throne during the lifetime of William Shakespeare (c1564 - 1616), were Queen Elizabeth I (1533 - 1603) and King James I (1566 - 1625).
The plague
fur trade