Does Pein die

Answer 1

Yes, Nagato (Pein), does die, but on his own. Naruto masters Sage Techniques, and is now able to go into Sage Mode. However, he mastered it better than Jiraya, and can do it without and major charges to his body. Using Sage Mode, he defeats Pein's six bodies, and searches for the real Pein. When he finds him, he chooses to go by Jiraya's teachings, and let Pein survive. Pein tells Naruto his story about why he is in so much pain, and Naruto still goes by Jiraya's teachings. Pein is touched by this, and gives life back to everyone who died in Konoha. Then, Pein dies because of the condition of his body. As a result, Konan quits the Akatsuki.

Yes, Pein does die. Personally i found it sad, because his last words were to Naruto. And he didn't finish his sentence:
"Naruto... this... is what you must face... The book... and you... It's like... someone... set this all up... Or... maybe... this... is... the hand of the real god... My role is over now... Naruto... you... can really--"

After his death Konan encases Nagato (Pein) and Yahiko's (the Deva path) bodies in paper and takes them back to Amegakure to be buried. She pledges Amegakure's allegiance to Naruto on behalf of Nagato, giving him a bouquet of origami flowers as a memento.