Outside unit cooling fan runs a few minutes and stops. Changed capacitor and worked a day or so and is now doing the same thing. When fan stops compressor still runs and fan is getting very hot. Is the fan motor going bad or could the new capacitor be bad as well, or could something be burning the capacitors up. How can I check the capacitor with a volt/ohm meter?

You need a new fan motor. Probably the bearings went bad from lack of oil. This can be prevented by oiling bearings once or twice a year, but once bearings fail it is too late. Buy new fan motor and cap to match if different from that that you already purchased. Check rotation. Some motors allow for reversing rotation so take in old motor to match rotation. You can go up on horsepower but not down. If you have a 1/3 HP motor you can get a 1/2 HP but it will cost more in electrical power, however, it will last longer. Oil it before installing with high speed oil and every year. DrTom4444