DUE TO THE REASON OF ROUGH DRIVING and lack of oil in pump....
Most likely it is low power steering fluid. Check fluid and see if noise goes away.
Steering fluid leak.
Low power steering fluid or defective power steering pump.
It will most likely cause problems with the seals that hold the fluid inside then you will spring a leak, this could be a costly mistake.
Many things can cause that, the simplest cause being lack of power steering fluid.
Overfilling a power steering system with fluid can cause overpressure. You may cause a leak in your lines or pump.
No, they are not compatible and it will cause damage.
You need to remove the washer fluid. You can siphon it out, or remove the power steering reservoir and dump it out. If you haven't had the car running , you may be able to absorb it out with a rag since it is probably floating on top of the power steering fluid. The problem with washer fluid is that it is not compressible and will cause poor steering reaction when it enters the steering pump. It may even cause a loss of steering.
Low of power steering fluid is one possible cause. I urge you to have this looked at by a professional. Loosing your power stering in a turn can cause a serious accident. Do not ignore this as it can be very dangerous. Funny cause Ion's have electric steering and have no fluid resevoir. The problem is in the motor unit, and it is not seerviveable. You will likely need an EPS motor assembly. (Electronic Power Steering)
Yes, something wrong in the rack and pinion can cause a loss of power steering fluid. The failure of seals in any part of the steering system can cause leaks. Further diagnosis is recommended to isolate the problem.
You should have no issues should you use a Sythetic transmission fluid such as Nulon Multi vehicle fluid do not use regular grade auto fluid this can cause power steering pump slippage and or failure
Check the power steering fluid level. Low fluid is the most common cause. If the fluid is ok then the pump may need a rebuild or replacement.