As a U.S. citizen, if I petition my parents who live in Peru, would it be an absolute yes that they would get the immigrant visa/green card?

Of course, no one can give you any guarantees without knowing the specifics of your or your parents' situation but, assuming there are no issues that could lead to them being ineligible for a visa, and assuming they are indeed your parents whose names are on your birth certificate, there should not be a problem with them getting an immigrant visa.

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. 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.

Assuming you are 21 or older, you can file an immigrant visa petition for them. If they have no disqualifying past immigration or criminal issues they should anticipate getting the immigrant visa/greencard. The timing question will vary by circumstances. It typically takes 6 - 12 months for an immigrant visa to be issued.

Yes, if you have the rights documents and the parents are admissible. The immigrant visa is generally good for 6 months.