Does air resistance affect the motion of a falling object differently when the initial velocity of the object is greater?

Yes. Even greater. Air resistance or drag becomes harder the faster an object goes. This is why when cars reach their max speed they don't accelerate as fast, because they are pushing harder against the wind. If I take a tennis ball and shoot it down a bottomless pit, a 400 kph, the drag will slow the ball down till it reaches terminal velocity. 

Depends on the object. Is it round? Is it a cube? Air resistance all depends on what kid of surface the object shows when it is falling, thus you have parachutes to stop your velocity from making you go splat.