Black people tan, but you wouldn't describe a black person as having a tan. And actually, i didn't give the exact wording, which was that she was "quite brown." This is not a description compatible with normally dark skin that has gotten darker.

There is at least one description that rules out Hermione being black (or red-headed, or albino, or otherwise non-tanning). She came back from break with a tan.

Just cousin. A half cousin would be a parent's half-sibling's kid.