It is public domain since in his time period copyright wasn't made yet, and even if it had been, the copyright would have long since expired.
As with all public domain works, it's important to understand that this strictly speaking applies only to the original text. An annotated or translated version is subject to copyright as if it were a new document.
No. There was no copyright law comparable to ours in Shakespeare's day. However, the introduction, preface, notes and so on which are probably printed with your copy of the play likely are copyright, since they are modern.
The play itself was published in 1597 and is therefore in the public domain. Specific editions, performances, adaptations, films, etc. may have their own protections.
Mercutio was stabbed at the public square in "Romeo and Juliet."
Mercutio
Romeo and Juliet (1935), Romeo & Juliet (1968) and Romeo+Juliet (1996).
Romeo and Juliet
Romeo and Juliet
juliet
After Romeo and Juliet married Romeo owned Juliet and everything she owed as well.
Tybalt in Act 3 Scene 1 of Romeo and Juliet.
The notion of "copyright" didn't exist until probably at the earliest the Licensing of the Press Act of 1662, so Romeo and Juliet was not copyrighted. Even if it had been, it would certainly be out of copyright now; Disney wasn't around to lobby Congress to keep extending copyright protection back then.
Romeo was a Montague, Juliet was a Capulet.