Cadillac Repair: 2004 Cadillac Deville Power Steering, cadillac deville, hydraulic lines

Question
My 2004 Cadillac has 63K miles, after the car runs for about 20 minutes and the engine speed is low, at idle, the steering becomes very hard to turn and chatters from the power steering pump. If I increase engine speed, the steering becomes easy again. I have been told it may be a power steering pump problem or some other problem with the steering that the hydraulic lines connect to ?

How can I check to see if it is the pump and how difficult is it to change ?

Answer
IS or HAS the CHECK ENGINE light ever illuminated while driving the vehicle and or has any other lights illuminated or any messages from the message display center ?.

What work or diagnostics of ANYKIND WHAT-SO-EVER have been performed on the vehicle trying to fix this problem ?.