Yes. But Romeo and Juliet apparently borrowed heavily from works from 1562 and 1582[1]. Since he wrote the play in 1591, both works would have been under today's copyright.
I hope this doesn't sound overly aggressive, but you don't seem to have a very firm understanding of how copyright law works. Derivative works are covered as well. You don't have to literally copy every piece of something with full fidelity to fall under it; borrowing heavily can be quite sufficient. For example, an unauthorized encyclopedia of the Harry Potter universe got stomped because it borrowed heavily from the Harry Potter books. It wasn't actually a copy of any book, but it took enough to get slapped down.
IANAL, but I personally have no doubt that Shakespeare would have been sued if today's copyright culture had existed then. He even copied the characters' names (and yes, characters can be covered by copyright), not to mention most of the major plot elements. It wasn't just "Oh, this general idea is kinda similar to that one."
It's the skill of Shakespeare's story telling that made him so great, not the stories themselves. But the stories are protected by copyright, not the skill.
Nonsense. It's still not possible to copyright the idea of a "love story involving two feuding families," or something. You can't copyright ideas.