Do my parents have to go back to their country even after they have lived in the US for more than 21 years?

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. What is the status of your parents? Are they here illegally? Is there someone who can petition for them. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case and advise you of your options.

Yes, unless they can obtain one of the forms of relief from removal available under the immigration law. A competent immigration attorney could give you a specific answer, but he/she would need in interview your parents to find out all the information about them that is necessary to determine whether your parents can qualify for any form of immigration benefits.

Depends on the facts and circumstances. If they entered legally, maybe not. Either way, they should never leave without a proper consultation with a qualified attorney. There could be a 10year bar to re-entry.

That will depend upon their immigration status and options.

Living here for 21 years by itself will not give your parents any benefits. If they did not sneak into this country, there may be more options. If you were born here, maybe you can help when you turn 21. Consult with a good immigration attorney to review all the facts and options.