My ABS light would come on intermittenly like that. It turned out my radiator was leaking onto the sensor. After I replaced the radiator, the light went away. I also found that it would get triggered when driving through a dust storm or a big puddle.

The check engine is usually fuel or emissions, and can be caused by the same thing..dirty 02 sensors. You might have a leak of oil or coolant..or even ac condensation that is dirtying up the guts of your car.

To clear the codes, try disconnecting the battrey for a few seconds. This will rest the computer. Make sure you have your stereo lockout codes!