The archetype say that Invoke Patron works like a Hunter's Animal Focus. Does that mean Invoke Patron affects the Witch's Familiar?
I don't see how. Hunter's animal focus doesn't talk about familiars at all.
Nope. If you had an animal companion, that would work, but not so much for a familiar.
Nope, familiars aren't animal companions, and vice-versa. Though, if you take the Animal Ally feat for a companion, then that companion would benefit from your focus abilities.