Why did Voldemort allow half bloods?

Voldemort didn’t want to get rid of Half-bloods he wanted to get rid of muggle-borns( Mudbloods). He was just obsessed with killing Harry Potter ( Blood status: Half -Blood) because of the half heard prophecy.

Why did Snape join Voldemort in the first place?

Severus started at Hogwarts with Lily in 1971, where he was Sorted into Slytherin House. This put him in the same year as Lily but unfortunately for him in rival houses. In an attempt to win back Lily’s affections, Snape joined the Death Eaters along with a group of his fellow Slytherins.

Did Voldemort’s Death Eaters know that he was a Half-Blood?

Canon seems to conflict a bit on whether Voldemort’s Death Eaters knew that Voldemort was a half-blood. In Half-Blood Prince, Tom Riddle refers negatively to his parentage and it reads as if his fellow Slytherins found it amusing in a derisive way, even though Salazar Slytherin was the ancestor of Tom Riddle (HBP – chapter 23 – Horcruxes).

Was Snape happy to be called a Half Blood Prince?

Snape was portrayed as if he was very happy to be called as Half blood prince. Snape named himself as half blood prince and nobody attempted to name him as such. Snape was found to have an idea of dissociating himself from his family name. Probably snape did not like his father as his father used to frighten his mother.

Why didn’t Voldemort kill Snape as soon as possible?

Snape wasn’t even pretending to be a double agent during Philosopher’s Stone, so why Voldemort didn’t kill Snape as soon as he was physically able, or have Quirrell attempt to kill him, is unclear. So yes, why didn’t Voldemort suspect Snape as a double agent during the events of Philosopher’s Stone?

What was the name of Snape’s mother and father?

The mother of Snape was called as Eileen Prince and his father was Tobias snape. One of his parents was wizard and the other is not. Snape’s father was muggle and his mother was a magical woman. As he was the product of a witch and a muggle, he named himself as half blood prince inheriting the surname of his mother.