2000 Chevy Lumina Hard to steer at idle

The problem I have been having is that my wheel is extremely hard to turn when I am stopped at an idle, or moving at very slow speeds (i.E. Parallel parking). It is almost as if there is no power steering at times. While driving, it steers just fine. I have also tested it when stopped, and have found that if I press on the gas just a little (up to 1500-2000rpms) the steering loosens.

It also seems to get worse as the car warms up. When I first start the car in the morning the steering (although a little difficult) is mostly normal. However, after driving a couple minutes, I notice the wheel tighten up when trying to park or maneuver at slow speeds (<5mph). I have also noticed a slight noise when turning sharp to the left at around 15-20mph (humming sound) and a persistent clicking noise coming from the front wheels that gets faster as I speed up. This may be unrelated, but I am curious about this as well.

I had a mechanic take a quick look at the steering this afternoon. From what he saw, he thinks it may be an issue with the rack and pinion steering, possibly requiring it to be replaced. I am taking it in for a full inspection later this week, as he didn't have time to look too closely. I simply would like some advice on what to expect, before I go and spend big $$ on repairs. Does this sound right, or could it be the power steering pump going bad?