It could be from worn bearings on the shaft that the pulley turns.
No. The power steering fluid has nothing to do with your cooling system. It goes from the reservoir to the pump to the steering rack and back again.
it can overheat and burn up
If the water pump is bad, it will leak and your car will overheat. If the Power steering pump is broken the steering will be very hard and if the timing belt malfunctions, your car will stop running.
A power steering pumps as much as the power steering pump can pump.
Bad power steering pump
Remove the power steering pump hose. Remove the power steering pump belt. Remove the power steering pump retaining bolts. The power steering pump will come off.
After bleeding the power steering the pump may make a noise because there isn't enough power steering fluid in it.
Secure the power steering pump with the retaining bolts. Attach the power steering hose to the power steering pump. Put the belt on to the power steering pump. Fill the power steering system with fluid.
None of the belt driven accessories will work : water pump ( and non electric fan )will not turn - so vehicle would eventually overheat power steering pump wil not pump - so no power steering alternator will not turn - so battery would not be charging air conditioning compressor will not turn - so no air conditioning etc.
Remove the belt for am your power steering pump. Remove the power steering pump hose. Remove the power steering pump retaining bolts. Reverse the process to install your new power steering pump.
Drain the fluid from the power steering pump. Remove the power steering hose. Remove the wiring harness from the power steering pump. Remove the power steering pump retaining bolts. Reverse the process to install the new power steering pump.
most likely your alero's power steering pump would be leaking from the power steering reservoir, but as an alero owner i have had to replace the whole pump because the pump shaft snapped on me