Can someone please answer this question: Since both Voldemort and Snape were both in Slytherin, but they they were not purebloods. So the main Вопрос that i'm asking is that does Slytherin except not just Purebloods?

Slytherin values ambition, cunning, leadership and resourcefulness and most of all pure wizard blood. Slytherins tend to be pure-bloods или half-bloods who believe in the supremacy of pure wizard blood; Muggle-borns, vulgarly known as "Mudbloods", are less commonly found in Slytherin than in other houses - It's from wiki :)
Snape and Voldemort believe in the supremacy of pure wizard blood and are ambituous, cunning...so that explains how they got accepted in Slytherin

Yes, I think it's the caracter of the person who count. In addition Voldemort is a descendant of Salazar Slytherin.

Actually, it сказал(-а) in the Книги that there are VERY few legitimate purebloods in all the Wizarding World. Most of the "purebloods" just disown their family heritage which is not of pure blood, but technically they aren't. They just claim they are.

Nobody knew that they were not purebloods so it was a secret that is why snape did not tell anyone that he was the Half blood prince and voldemort killed his one muggle parent.

they accept pure-bloods, half-bloods, and (very rarely) muggle-borns