No there was no horcrux in voldemorts body. The only horcruxes were the snake, the hufflepuff cup,tom riddles diary ,the ring,the locket,the diadem, and the fragment attached to harry. What was in voldemorts body was the last bit of his soul that he didnt turn into a horcrux. So after all the horcruxes were destroyed all that was left was his last piece of soul which harry destroyed (:
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Voldemort split his soul into eight parts - seven into his seven Horcruxes, and the last piece was the piece remaining in his physical body. His horcruxes were;Tom Riddle's diary,Rowena Revenclaw's Diadem,Helga Hufflepuff's Cup,Marvolo Gaunt's Ring (Voldemort's maternal grandfather's ring)Salazar Slytherin's locket,Nagini (Voldemort's snake)Harry Potter (Due to back firing of the killing curse)And Professor Quirrell was not a horcrux.
It didn't hurt because he looked at Snape. Professor Quirrel was right next to Snape, and it was Quirrel that made Harry's scar hurt because he was sharing his body with Voldemort. His scar hurt because the Horcrux inside Harry could sense Voldemort and was attempting to leave Harry's body.
Little Hangleton was a muggle town where the Gaunt family (Voldemort's mother) and Riddle family (Voldemort's family) lived. Voldemort himself, never lived there. His lived his whole childhood in a muggle orphanage. Voldemort did spend time in his grandparents old house when he was working on getting his body back. There is no mention of Dumbledore ever living there.
Peter was supposed to kill Harry Potter in Malfoy Manor, as Harry was trying to escape, however he hesitated and his own silver hand, given to him in Goblet of Fire by Voldemort, strangled him to death because he showed weakness.
AnswerThe exact curse was never specified, but it was caused by him wearing a cursed ring.AnswerAvada Kedavra, cast by Severus Snape. But he was already poisoned and cursed, so he would have died soon anyway.