To me it sounds like you have bought a faulty radio. That is one thing i've learned through my years going to junk yards. Never get a radio unless the car just got there.

I got the factory radio out of a 90. 100% works. it was still in it when i bought the car . let me know if you want it. pay shippin and you can have it

Don't have any suggestions for the static but my radio was only playing on one speaker but on bumps it would play the rest of the speakers so I knew there was either a short or loose ground. So just last night I added a ground wire to the radio using a bolt that was already on it then screwed that in to the metal frame where it gets screwed in but on the back side and now It plays both the front speakers. I'm thinking there might be a wiring issue for the rear because I've never heard them. I'll look into that some more this weekend. Maybe a good ground will help you. Also check the connection of the antenna in the back of the car.