That squeak you can hear and feel when turning is caused by the seal for the input shaft on the rack(i.e. the pinion). It is due excessive friction between the seal and the shaft. There is a repair kit for this, I only recommend letting a technician do it because you must disassemble the rack and install new seals and apply a special lubricant, special tools are also required. This repair kit saves a lot of money compared to replacing the rack. You will probably notice the noise gets worse after driving for awhile, it seems to be affected by temperature. And yes, it will normally only do it with the engine running, because that is when pressure is applied to the seal by the power steering fluid behind it. This seal is there to keep the fluid in the control head of the rack(the part that makes the steering "power"), without it the fluid would just blow out of the rack(hence why you must never install the seal backwards!)