Power steering shuddering badly?

Tonight I jacked up the front and made sure the reservoir was full. I did not run it at first, I turned the wheel back and forth for about 20 minutes, (still seeing bubbles) then I ran it and filled up the fluid to make sure I could not see the pump. Because last week, I could see bare metal at the pump which I thought was odd. This time I purposely filled it up too much to make sure I could not see the pump through the filler hole. The fluid went down quite a bit and so I filled it up as it ran. I turned the wheel while running and the steering still shuddered, and this time there was foamy fluid. Then I turned it off again and the fluid spilled up and out of the filler tube and all over the floor. I then turned the wheel again while it was not running and saw less bubbles. Then I ran it again and repeat above.
I bled it four about one hour tonight. I am going to let it sit overnight and do it again tomorrow and I will do this until there is no more shuddering. Thanks for your help!

The pump is new, FYI.
I tried again tonight, and it is shuddering so badly when I turn the wheel, it is undriveable, and I am really just getting nowhere. There are still bubbles coming out of the reservoir when the truck is off, and I turn the wheel. There is foam when the truck is on, and I turn the wheel. But like I said, it shudders so badly I have to turn it off. I might put the old steering rack back in because maybe this new one is faulty. Or maybe the new pump is bad? The power steering is very quiet, so it's confusing to me why it won't bleed. Everything is tight. 6pm now. I have discovered while turning left, the vehicle shakes violently and turning right it is perfect. Now I think the Steering Rack is bad. So I am going to take that out and put the original one back in. What do you think?

I swapped the rack and it's okay with no weight on it, but when I lower the truck to the ground, it shudders in both directions when I turn the wheel. I guess it's the pump. I checked the hoses and put on EFI clamps on the return line and on the oil cooler.

Okay, brand new pump is in and the problem remains. I drove it around tonight and took a left hard turn in my cul-de-sac and it started to make bad whining noises, so I turned it off and looked at the reservoir and there was still foam in the fluid. I can't figure out what is wrong now.

I replaced the rack (Detroit Axle) and that one did not work; I replaced it with the original rack. I installed a new pump, then I replaced that thinking it was bad with another new pump. New hoses, EFI clamps, new high-pressure hose, new low-pressure hose. Teflon fittings are new. The Teflon seals were a little easy to get on, but I don't think that is the problem. If I let it sit, then jack it up and turn the wheel, more bubbles arrive out of nowhere. I think the problem is that it is sucking in air, and I can't figure out where it's coming from. I tried to do the vacuum test, but I can't find a good adapter that fits, I ordered 3 different ones and none of them fit in the reservoir filler tube. So, I used some tape and wrapped it around the fitting and jammed the fitting into the reservoir neck and it was tight, but putting vacuum on the pump shows 2-5 psi or less and goes back down quickly.

Okay, so it appears I have been bleeding this wrong. When I run the truck, the level goes down. While it is running, I have been adding fluid because I can see the metal housing (slightly). Then when I turn it off, it overflows, and air is in the system. My research shows that I should only fill it when it is not running, or it will chop up the new incoming fluid and introduce air into the system. Does that sound correct? Am I doing this wrong?

Yes, I had the truck running while adding and that was not a good idea by me. Now I have finally fixed it. What I ended up doing was buying pump #3 and I installed that. At first it did not work. In the morning, I had the idea to run the truck, turn the wheel all the way to the right and turn the truck off. I let the truck sit all day while I was at work. That night I came home I ran the truck again and turned the wheel all the way to the left and turned the truck off. This time I let it sit for 20 minutes, then I turned the wheel back and forth while running and suddenly it stopped shuddering and started working perfectly. Thanks again!