Kind of human but still immortal I guess . Taking his magic and his immortality are two different things.

No. Still a warlock. There are actually magic-less warlocks, called ifrits, at least in the books. Even if the show doesn't decide to tackle ifrits, it's still not just his magic that makes him a warlock, its his parentage (the fact that he's half-human half-demon).

no. he is still a warlock.

Wouldn’t he also still have his cat eyes, making him a warlock?

yeah

I think he would just be a demon.