Is Hermione Granger a muggle or muggle-born?

Answer 1

Yes.

To be pure-blood, both parents need to have been born by pure-bloods and to be muggle-born both parents need to be muggles. Neither was the case for Harry whose father was a pure-blood and mother was a muggle-born which makes him a half-blood.

Answer 2

Yes. His mother was a pure-blood witch and his father a muggle.

Answer 3

She has two muggle parents, so she is muggle-born. ("Mudblood" is an offence word, decent people never use it.)

Answer 4

Hermione is a muggle-born witch. If she was a muggle she wouldn't have been able to cast spells.

Answer 5

No, He is a pureblood.