Recently my truck start to make a groaning sound from the power steering pump reservoir at low or no speed. It sound like the noise it makes if you turn too hard and hit the stop. (The answer to your first question is No.I don't do this often). This suddenly started with no warning. Steering is find. When truck is moving, noise is minimal but, slightly present. I flushed the system and replaced the fluid. Bled the system for air. Checked tire pressure. Checked for collapsed, crimped or bad hoses and leaks. All negative. The belt is only a year old and looks great, plus when the A/C is on, I get no squealing like you would from a bad belt. Could it still be the belt? The Pump and steering rack are the last things to be ruled out. Is the any way to check to find out which one it is?
The noise you describe is often associated with the pump pressure relief valve, when you hit the bump stop the pump is still delivering pressure and this is when the relief valve opens, you do find faulty relief valve "groaning" I would get the pump pressures checked this will show if the relief valve is leaking or not.