Oh good questions. First one I don't know.
About an indoor kite. Indoor kites do better indoor. 0 wind kites usually are super low wind and will also work indoor. Indoors are really meant for indoors. A gust out of no where could damage an indoor kite. Not to say we haven't all flown our indoor kites out side.
Indoor quad really you best option is a rev. If you can find a synergy deca they are the nicest quad I have seen but are no longer made and harder to fly. Indoor rev is usually what people get as it's the only one made at the moment I believe.
A stunt kite can be used of any kite that can be maneuvered really. Quad or dual line, indoor and out. And sport kite and stunt kite I have both heard for different reasons. Rev is often used to describe any quad line kite like chap stick it's a brand but used wrong a lot. It's usually just dual or quad but fighter kites are in there as well and probably take the highest skill.