Will a 200mm F4 AI work with a Nikon FA?

Looking for a good lens. Do they make some that do 35mm and zoom? Is a zoom lens a telephoto lens? And does that lens only do 200mm?

Any AI lens will work with an FA, but AIS lenses will give you the most features. Can't remember exactly what it is that you lose by having AI instead of AIS but I don't think it's too much.

The lens you list, or any other single focal length lens, is called a prime lens. A lens with multiple focal lengths is called a zoom lens. 80-200mm is a very common zoom - it will be 80mm on one end and 200mm on the other. Lots of versions of this type of lens, may be 70-210, etc., different apertures and AI, AIS and AF (auto focus). Not all zooms are telephoto though - there are "mid range" zooms like 28-105 and wide angle zooms like 20-35.