do the components of projectile motion affect eachother?

Answer 1

The assumption in most physics problems is that they do not. But force due to air resistance depends on v^2 =vx^2+vy^2 so the x motion will depend on vy and the y component on vx if air resistance in the problem

Answer 2

no
x component is motion with constant velocity
y component is motion with uniform acceleration

Answer 3

x is constant assuming air resistance is negligible

y is constant acceleration assuming vertical distance travelled is small enough to assume acceleration due to gravity is constant (i know that's a bit pedantic)