Quirrel couldn't put his hands on Harry without getting burned because he was sharing his body and soul with the spirit of Lord Voldemort at the time, and Lily Potter's death invoked a powerful blood-magic that prevents Voldemort from causing Harry any harm.
He asks Dumbledore again about the stone and Dumbledore tells him that he arrived just in time to save Harry from Quirrell. Dumbledore adds that he spoke with Nicolas Flamel and they decided to destroy the stone. He explains also that Quirrell could not touch Harry because Harry was protected by his mother's love.
As Voldemort was possessing Quirell at the time, the spell started working and burned Quirell's body when he touched Harry. If Voldemort was not present in his body - Quirell would not have had any difficulty to touch Harry. It was solely because of Voldemort that Quirell's body burned.
In the books it says that Quirrell shakes Harry's hand, and this doesn't effect him because he isn't yet possessed by Voldemort. In the movie however, he has his turban on and we can only assume that he is possessed by that point.
When they met for the last time in the final of the Philosopher's Stone Chambers, Quirrell's connection to Voldemort rendered him unable to touch Harry without experiencing unbearable pain, due to the enduring power of Lily Potter's sacrificial protection, and he died attempting to steal the stone from Harry by force.
As for how Voldemort got onto Quirrells head, it is unclear, but some think it might be because Quirrell had made a blood pact with him when they both were working at Hogwarts. Quirrell was unable to resist Voldemort's will and was forced to do his evil deeds.
It should be noted that despite his fear of Voldemort and that he was not a Death Eater, Quirrell was one of Voldemort's only followers who referred to him by name, the others being Barty Crouch Jr. and Peter Pettigrew.
Snape did not need to tell Dumbledore about Quirell because he already knew. It was Dumbledore who told Snape to keep an eye on Quirell because the former already had his suspicions. Snape was not able to accumulate solid proof but otherwise Dumbledore was well in the loop.
Quirrell didn't use the Killing Curse on Harry, because Voldemort said “use the boy” to get the Sorcerer's stone from the Mirror of Erised.
Snape and Quirrell taught together at Hogwarts at least one additional year prior to Philosopher's Stone, although Quirrell's employment history at Hogwarts is murky. Quirrell is described as a "young man" but his precise age is unknown, while Snape is canonically 31 at the beginning of the first book.
The most likely reason why Lord Voldemort's nose disappeared and he devolved into such an evil-looking creature is that as he dabbled deeper into the Dark Arts, his appearance gradually became as distorted as what remained of his twisted soul.
Voldemort intentionally made six Horcruxes, but when he used Avada Kedavra on Harry, he unintentionally created a seventh Horcrux. Instead of dying, Lily's love for Harry created a counter 'curse' known as Sacrificial Protection and saved Harry.
There is also a strange smell of garlic that hangs about the classroom; the Weasley twins insist that it is because Quirrell has stuffed his turban full of garlic to ward off vampires.
A Professor at Hogwarts School of Witchcraft and Wizardry, Snape is hostile to Harry due to his resemblance to his father James Potter, who bullied Snape during their time together at Hogwarts. As the series progresses, Snape's character becomes more layered and enigmatic.
Ramitha Reddy Voldemort and Harry had core wands. Their wands had a phoenix feather from the same phoenix, Fawkes. So, Voldemort did not have full control over his wand.
Hermione did not grow up in the wizarding world but she did hear and also read a lot about Voldemort and his death eaters. This is why she was afraid to say his name. But Hermione is the first of Harry's friends to use Voldemort's name. She begins to use it in the fifth book.
So basically a combination of factors: Snape explained to Voldemort that he was ever faithful to him. Snape had 16 years of information on Dumbledore to give to Voldemort. Snape also had information on the Order to give to Voldemort.
In order to conjure the avada kedavra curse, you have to want to kill your victim. We all know that Voldemort could easily kill a child without an ounce of remorse... but not Snape. Snape didn't want to kill Dumbledore, and this was why the spell was blue instead of the usual green.
In a way Voldemort killed himself as his own spell backfired on him. In Harry's fourth year Expelliarmus did not beat Avada Kedavra but Harry and Voldemort's wands recognized each other as twins and connected with each other in one mystical way that only a wand-maker could understand.
He doesn't trust Snape as Dumbledore does, but he believes that he can detect any disloyalty. Moreover, Voldemort regards Snape as highly intelligent and therefore ' as a true Slytherin ' a person whose top priority is to take care of himself. To his twisted mind, selfless equals stupid.
Voldemort's desire to beat death and become immortal was also why he and Quirrell ended up slaying innocent unicorns. Drinking the blood of a unicorn would keep someone alive – even if they were an inch from death.
He was on the point of collapse when it happened,” Rowling said. “Dumbledore didn't want to lose his wand at that point and Draco disarmed him. So that meant that the wand gave Draco its allegiance, even though Draco never knew it, even though Draco never touched it.
Following Voldemort's fall, Snape made no attempt to find his master, for he, like other Death Eaters, believed that Voldemort was dead, and he could use Dumbledore's protection to avoid being sent to Azkaban.
According to Voldemort, his essence could not be killed due to his creation of Horcruxes when he needed to take on a physical form, and naturally he could not return to his own body, he was able to possess living creatures and did so with animals on occasion.