Ok... lets keep it simple here. 1st off, the brown and the brown/white wires should have terminals on the end of them. They go to the run capacitor the guy gave you... one wire on one side of the capacitor and the other wire to the other side of the capacitor. Now your black & white wire are the power wires to the fan motor. Wire the black wire to one side of the contactor and the white wire to the other side of the contactor. This gives you your 240vac for the motor. Now mount the capacitor somehow or at least wrap the terminals(wire & all) with some electrical tape to keep them from touching some metal. **** Please make sure the power is turned off, as it can kill you ******* Hope this helps

It could be the coil pitched the wrong way, the unit not level, a crack in the condensate pan, not a deep enough trap, condensate line pitched the wrong way, a stand pipe on the wrong side of the trap. Water leaks are tough to diagnose without actually being there bit those are some of the things I've found over the years. When you shut the system off after its been running for a while is there a rush of water dumping into the condensate line?

It could also be a bad capacitor. If you have never fixed a condenser then it would be best to call in a qualified HVAC tech.

Thanks for trying to give us a drawing but it really doesn't detail how things are hooked up. From the sounds of it, you have something cross wired. Can you read a volt meter? how many volts do you have between the ground wire and the box? The reason I ask is the breaker should have tripped. If you have a lower than 108-125 volts, theres a short in one of the loads. Since it wasn't happening before, it's got to be in the new fan or, the circuit you are adding.