Sounds like the power steering pump has issues. Mine whines all the time, several others I know of do also, but then there are some that dont. Just a Ford thing with power steering pumps.
The way you describe the shaking it seems it is doing it when idling or sitting still ... which sounds like maybe the drive belt may be worn and slipping when the motor is running slow... but it could be other issues from a tie rod end worn to a worn ball joints also. You need someone that live near you that is mechanically inclined to check it out while you turn the wheel, it's hard to diagnose for sure without actually seeing and hearing it.