A/C Help, is it the Switch or the Capacitor or both?

Capacitors are cheap. Buy another and replace it and see if that'll get you fixed up. Yours looks like poo anyway.

it isn't the capacitor. fan motor kicking off on thermals. don't mess with electricity if you don't know what you are doing.

Doesn't sound like a capacitor, usually when they go, the unit will not come on at all. However, it wouldn't hurt to change it out, as they are cheap. It sounds like a relay could be overheating and shutting the condenser off. When the relay cools, it allows the condenser to come back on.

I should be studying for Circuits right now.

90% of the time if the capacitor is bad the top will bulge up (terminal area). If not and if you have a volt meter with a farad scale you can see if it working fan will be 5 and the compressor be 45. Sound like a thermal internal trip on your fan for the outside unit. Have you cleaned the coil recently. Could be a high pressure trip on the compressor

Have you checked to be sure it is not something like drip pan filling up after it runs for a while and kicking off the level switch?

WPB, is your air filter clean, is your condenser coil clean and is your evaporator coil clean? These are what you can see for yourself. There are many reason why this could be happening. You're not getting 24 volts to your contactor, which means something is causing something else to trip and not send the 24 volts down line to pull in the contactor. If your compressor builds up high pressure, then it will trip a high pressure sensor, thus causing the contactor to stop pulling in. Beyond the obvious reasons stated above, you probably need to get a professional out to diagnose the issue.

Mine runs a while then the blower stops, I think it's freezing up. Do I need freon ?

Check to see if your pan is full of water. If it is it won't send a signal to pull the contactor.