I've searched for weeks, but there's a lot of contradicting information out there.

Power Steering Issues
Problems:
Groaning when turning, slight or extreme, sound is coming near the reservoir/pump area.
Steering can be really hard, almost feels like power steering is failing, when just starting off.
Fluid looked a little foamy when it was hot. But the fluid level has not budged and there are no signs of leaks.

I'm thinking there might just be a loose hose or something that's letting in air; cause for the bubbles.
As for the groaning and hard time turning, pump failure? Really hoping it's not the whole rack.

It has been around freezing this month, when the problems have really escalated.

Rough Idle when Transmission Engages
I cleaned out the throttle body, that made a huge improvement in throttle response and how smooth the car runs. But it still idles rough in Drive or Reverse (not Neutral or Park) and feel rather violent when first starting off, 0-5mph.

 

Update:

I ordered a refurb pump (with attached pulley and reservoir) off e-bay, $28 shipped.

Install was a bit of a pain without a proper tensioner tool, but we made due.

I drained all the power steering fluid at that time, it was still fairly red in color but I topped it off with fresh.

Steering groan is gone and there is no more difficulty when turning. There is a slight hum from the pump, but I'm blaming that on it being a refurb and an older part in an older car; it's nothing like the hideous groan it was making before.

 

What do you mean by idling "rough"? Is it idling too low and causing excessive vibration, or is the idle fluctuating? Or both?

How does it idle with the AC on vs off, or when the steering is turned and held at full lock?

The reason I ask is because I have experienced what a bad or disconnected MAF can do to the car's ability to idle. If your car is having MAF issues, the idle can slow well below normal and cause the car to shudder if load is put on the engine at idle, like with the PS pump at full lock or the AC pump running, or in your case the TC engaged at idle when the car is stopped.

Basically, check the MAF, it is a possible cause for a "rough" idle.

 

I checked the MAF and throttle body first. Both have been cleaned and are working fine.

"Rough idle" might be the wrong way to word it. There is no fluctuation in RPMs, the car is simply vibrating when stationary in D or R.

 

In that case, it would be a good idea to check your engine and transmission mounts. Broken/collapsed mounts can certainly cause increased vibration that can be felt throughout the car.