You are correct. "Vil ha" means both "wants" and "will have". It's a strange word, but Norwegian has plenty of these. I find myself asking my Norwegian boyfriend about these kinds of things all of the time, and he just says, "Yea, Norwegian is weird." Btw, I answered it the same way, and I got it correct.
"Har" is the present of the verb "å ha" (infinitive). You use "ha" if: it is next to an auxiliary verb (like "vil", "skal", "kan") or any other verb or if you are using it in imperative.
Jeg vil ha - I will have/I want to have Jeg kan ha - I can have Jeg har - I have Ha de (bra) - Have it (good) = (good)bye
(I'm not a native, but I'm pretty sure this is the difference)
No, one would never say 'an horse'. One would say 'an habitual occurrence', 'an historical text' and 'an heroic effort', however (but 'a habit', 'a history lesson' and 'a hero'). If you try saying 'a habitual' versus 'an habitual' etc., you will hear that the former sounds strained and awkward.