"You want a horse."
Translation:Tu veux un cheval.
I'm no expert, but from what I've come to understand. 'Tu veux un cheval' is more of an informal expression. While 'Vous voulez un cheval' is formal. Both are grammatically correct. It just depends on the context (and preference) where one might be used.
It should be 'voulez-vous un cheval?' but yes you can (or Veux-tu un cheval?).
There are a lot of ways to ask questions and the inversion is the most formal and the least used. It is more common apparently to simply say 'Vous voulez un cheval?' and raise your voice at the end which makes it a question.
Or you can also say 'Est-ce que vous voulez un cheval?'.
In English, both plural and singular second persons are "you." So "Vous voulez un cheval" makes sense as well.
For vous, the verb should be 'voulez'
While you can also say "tu veux"
No, that would be incorrect conjugation. Je veux, tu veux, il/elle veut, etc.