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It will work for putting on waxes or sealants. You will need something with more speed to do paint correction though. The Porter Cable is the way to go!
Without seeing your car I can't tell you if it will completely. If the spiderwebbing isn't too bad it should remove them. I've corrected some pretty bad paint with the pc.
When you polish to get rid of the swirls most likely it will take care of your oxidization problem too. Again, it is hard to give a complete answer not seeing the car.