In English, we use 'have' in all three examples, but in Japanese you need a different way of expressing each of these things.
to have an inanimate object is 持つ 「もつ」。車「くるま」を持って「もて」います。 I have (own) a car. Bu t you can't use this verb to describe owning an animal. For that, it is 飼う
「かう」 - sounds the same as the verb for 'to buy', but different kanji. ねこが三びきを飼っています。I have three cats.
The have in 'have to' is different again. You express the idea of having to do something by conjugating the verb of the action involved. So have to go is 行かなければなりません。I found this confusing at first, as this is what we call in English, a double negative, and as we all know, in English at least, double negatives are generally frowned upon. However, I came to think of this as meaning 'if you don't go, it won't be okay' - therefore, you have to go. Japanese often seems to come at something from a very indirect way, whereas in English we are inclined to get straight to the point! I hope this is helpful (and I really, really hope that I haven't made any mistakes with my Japanese). Good luck - がんばってください。