I have personally never heard of "stains" for coloring swimming pools. you can however have your pool resurfaced. there are many different options to do so. My personal favorite is called "diamond brite". it is a prety smooth surface, and is availablr in many different colors!
yes
You drain the water then plaster the walls from inside
No, salt does not damage the plaster. Improper water balance will.
Yes, plaster will dry out and crack.
no
No Plaster of Paris is too soft and too porous to be useful in any thing to do with a swimming pool.
Color loss of what? You didn't specify loss of color on what. Tile, deck, plaster, clothing. In any case chlorine would be a more likely culprit.
Is the water rusty color? Or is the rust color on the pool finish - plaster or vinyl or fiberglass?
The water becomes aggressive and can etch the plaster and metal parts of the pool and equipment.
First you have to determine if is in fact a painted pool. If it is a plaster pool then usually there is no paint unless it was painted because of age and damaged plaster. You most likely do not want to paint a plaster pool - have it acid washed to clean plaster. Not sure how to determine what type paint. You would have to have the paint chips anaylized to determine if it is a chlorinated base paint or epoxy paint. Ken
It is know to be concrete, gunite or shotcrete.
The best color would be your choice of a new plaster finish. Why would you want to paint a pool???
Yes...any concrete grout will work.....you're better off regrouting though because chances are that the grout is sealed and the stain will only last one or two seasons.