1. What happens to air resistance in problems involving projectile motion?
In the mathematical treatment of projectiles, at this level, air resistance is ignored.
2. What effect does gravity have on projectile motion?
The only force acting on the body is that of gravity. There is no horizontal accelaration acting on the body and therefore the horizontal velocity remains constant.
There is a constant acceleration for the vertical motion of a = -g which is due to gravity.
3. Is the variation in the force of gravity, due to altitude etc, taken into account?
Any variation in the force of gravity is ignored in the mathematical treatment of this type of problem at this level.