Based on the nature of your questions it is obvious you are new and completely unfamiliar with this process. It is highly recommended you consult and recruit an expert in the visual effects arena.
It is possible for an individual to do it themselves, but it is a steep learning curve and not worth the risk of wasting precious time and money on ignorant mistakes.
Green screen
1. Yes you can move the camera, but it will complicate compositing the background.
If you restrict the camera movement to pan and tilt only its not so difficult to track. If you move the camera on a dolly or hand-held, then it gets very complicated. In any case, you have to record some form of reference data to establish the camera position. For a static lock-down camera you need to note the camera's height from the floor and tilt angle, and roll if there is any.
If you move the camera you need to mark the green screen with some kind of reference objects that the camera can see. These will be used to track the camera movement in post. Any sort of random symbol placed at regular intervals will do. Then the symbols must be measured. This is usually done with a surveyor's transit. Any other objects in the shot should be measured also.
These rules generally apply to shots requiring a CG background. If you are adding a live filmed background it is more difficult to do moving camera shots. That requires motion control cameras or a synthetic background plate constructed of stitched still images. Very complicated.
Research Matchmoving or Camera Tracking.
2. This is the compositing process. It requires capable software such as After Effects and some knowledge of the process. Impossible to explain here without writing a book. Consult a book.
3. Yes. The more of the set you build on stage the less you have to create in CG. It also provides the actors with some sort of spacial reference.
4. Yes you can film the backgrounds yourself, but you need to know what you are doing. Generally you cannot move the camera. You need to shoot the backgrounds at the same camera height and tilt angle as the greenscreen elements, or vise versa, depending on which was shot first.
CG
1. Google Compositing software, 3d Animation, Matchmove or tracking software.
2. 3d animation. An whole other subject too big to discuss.
Find an effects professional. You are in way over your head.