The power steering chatters when I first start the car and start a turn. Once going to steering is fine. Do you know what could be causing this?

Was your brake pedal on the floor or hard to depress? Your chattering might be the serpentine belt system. Remove the belt and test quickly again for noise, you will not have powersteering or cooling or charging systems, but you are just trying to pinpoint your chattering so you dont have to guess. You might want to replace your vacuum valve at power brake booster if your pedal was hard. It is a oneway valve that opens when the car gets turns on and pulls down a vacuum to assist the brake system. Sometimes the stick. If your brake pedal was on the floor, which I doubt at all, do not drive and seek professional help. Maybe your pedal assembly is coming loose and needs repinned.

It could be caused by the bearings in the pump going out if your sure that it's the power steering.

check all linkage arms under car. make sure all rubberr seals are there and armsare connected

check belt is tight and or not damaged if good check power steering fluid if low can cause binding if good have alternator and battery checked alternator may be going bad and not charging battery [and if bearing going bad can cause binding }

Did you have the trouble codes read? If not, then you're just guessing and that's no way to diagnose the problem.

Peel back the carpet on the driver's side and check for water stains. If you have stains along with trouble codes C0475 or P2138, you'll have to fix the leak in the roof channel and possibly replace the module or the motor. Check this service bulletin
#PI0116A

i think it might be ur rack and pinion going bad

You may be entitle to a campaign about ESC/steering module relearning, what happens if you leave the key in the ACC position for 2 seconds without starting the ESC is disable until you restart the vehicle. Here is the letter to owner number 07224A070911-005 , Hopefully this is still active and they should not charge you anything

bad power steering belt.

As far i can see the problem of your car is that the idle. Some cars use to be like that i have encountered that once. I went many car checking but when i found out its the idle . If there is other problem on it that is the steering .While you turn the steering there is a wire that is disconnecting to the ignition switch . While you turn the steering.Adjust the idle if that is the problem . if there is a wire disconnecting check and connect it ,good day.

Just guessing. Could it be a warped brake disk? That would cause vibration. And vibration in steering might conceivably cause splashing out the power steering reservoir. You would know if the disk were warped by a shudder when you brake at hight speeds.