Does A Permanent Resident Needs A Mexican Passport To Travel To Mexico?

Not you don't need a Mexican passport, only your temporary or permanent resident card ( Green Card ) , but if you want to take a Mexican passport , you can go the any Mexican Consulate, call it and ask what you ID's you need to get a Mexican passport , for the general you will need your Mexican Birth Certificate, 2 pictures, prove of Drivers Licence or State ID, your ( Green Card ) and they will give you your passport the same day. It is good that you make an appointment before, they will give you the date you can go to get your passport

No you do not need one the card is enough

Eve if you are have a peruvian passport?

You didn't mention your permanent resident visa. However, you don't need the passport of the country where you want to go. You can use your country passport. Just visit the consulate or embassy of the country where you want to go for the information.

I'm a permanent resident of the state of Nevada I was told I need a Mexican Passport to return to Mexico on vacation is that true? If yes how do I go about getting a Mexican passport?

You can get your passport but in mexican because the reason that you are a resident not a citizen of the united states