After 1594, Shakespeare wrote all of his plays for his theatre company, The Lord Chamberlain's Men (later the King's Men). It was the acting company that owned the script.
Yes, he did.
Shakespeare borrowed from Ovid's "Metamorphoses" and Chaucer's "The Knight's Tale" to write "A Midsummer Night's Dream." These works provided the inspiration for the magical and romantic elements found in the play.
Almost all of Shakespeare's plots are borrowed from elsewhere. The only original "tales" are The Tempest and A Midsummer Night's Dream.
In the 1590s, probably around 1594 or 1595.1594-1596
A Midsummer Night's Dream
A Midsummer Night's Dream does not have an Introduction, at least not the way Shakespeare wrote it. Usually the editors of a particular edition of the play will write an introduction to it, but that's not Shakespeare, it's not part of the play, and it's different from edition to edition. The only Shakespeare play which has an Introduction (it's called an Induction) is The Taming of The Shrew. Some of them (Romeo and Juliet, Henry IV Part II, Henry V, Pericles) have Prologues, but A Midsummer Night's Dream doesn't have one of those either.
Shakespeare did not as a rule write "stories". He took other people's stories and made them into plays and poems. There are only two of the plays and none of the poems which have a plot which was not lifted from something else: The Tempest and A Midsummer Night's Dream. Midsummer Night's Dream is the earlier.
Shakespeare wrote all of his plays for the same reason: it was his job. He was a professional playwright. He could have had other reasons as well. Likely, he enjoyed the topics that he wrote about, and he thought that the parts would be funny and give the audience a laugh. He also often wrote specific lines into his plays that would make his benefactors pleased.
He wrote it for his acting company, The Lord Chamberlain's Men, who owned the rights to it. It is thought that it was performed at the wedding of some unknown couple.
Yes he did.
Opinions vary. It was one of his earlier plays, possibly at about the same time as Romeo and Juliet and Midsummer Night's Dream, in the mid 1590s.
Actually Shakespeare wrote very few stories. Most of his plays were written using stories other people had written. The stories he did write, like A Midsummer Night's Dream and The Tempest, were often fairy stories. He also wrote The Merry Wives of Windsor, which is a bawdy farce.