You can find stainless steel philips head replacement screws for the m/c cover at Ace or your local hardware store.
If the piston won't push back fairly easy, you can pop the piston out & clean everything. Just wrap the caliper in rags & slooowly compress the brake lever until the piston pops out. Then take the caliper loose for cleaning & reassembly.
To bleed the system, get a piece of clear tubing & put on the slightly loosened bleed screw, running the other end to your m/c reservoir. Fill the reservoir enough to keep the tubing below the fluid & slowly compress the lever repeatedly until you see no bubbles in the tube & the lever has resistance. Close the bleed screw, remove the tube , & put everything back together. This will give you a good brake without the PITA this usually is.
Now after applying & releasing the brake, make sure the bike rolls freely with no drag. If there is a drag, it's cheaper to get another caliper from one of our forum members than buy parts to rebuild.
Disclaimer: The above only represents my experience, yours may be different.