Do aunts and uncles have visitation rights?

Usually not. Its only recently that grandparent rights have been affirmed. If the parents are not allowing the aunt and uncle to visit, not much they can do. They can try going to court, but I doubt if their case will even be heard.

Not usually, unless they are a court-appointed guardian.

I would agree with the answers posted to this question. One thing you might consider is trying to find a family law mediator in your area, and arranging a "family meeting." I facilitate these in my town, and the rules are simple: anyone in the family who has an interest or something to say can come; all must be polite and respectful; everyone gets heard; laws are there if people have questions, but the law does not necessarily have to govern what the family decides to do. These meetings work particularly well when there are step-parents, new teens in the family, etc. At the end, we make a written agreement or "contract" that everyone signs and gets a copy of. It's not therapy, it's communication. Just a suggestion...