The relief valve is set. Yes, there is a filter inside the reservoir. There are two sizes of filter so before ordering a new one measure the old one to be sure. Why do you want to increase the pressure?
If the PAS is not working properly it could of course be the pump but also you might be losing actuation of the spool due to wear in the pins, yoke or steering arm or anywhere else in the system. Have an assistant turn the steering wheel back and forth and examine all components closely particularly the main vertical shaft for wear in its bushes. Any lost movement will reduce efficiency.
DavidP, South Wales