Is Hope Mikaelson Immortal?

No, she isn't Immortal. If she does, she wouldn't age, and we all know she ages. Yes, she has Vampiric blood in her veins, but that's about it. Hope is basically exactly like a human fed/injected with vampire blood, the only difference is that she naturally generates it.

Can hope Mikaelson be killed?

Hope is technically a Tribrid (a triply-powered hybrid gifted with the abilities of a werewolf, a witch, and a vampire all in one). ... Hope has yet to die or be killed, and she can only activate her vampire abilities once that happens since vampires are by definition undead.

Can hope Mikaelson die of old age?

Yes she'll probably age at a normal rate seeing as how she's part-witch. The only way she can stop aging if she becomes an immortal hybrid. Hope is a witch-werewolf hybrid, who has vampire blood in her system from Klaus being her father (the blood wont leave her system, as she is born with it).