Both the fan motor and the capacitor are new.

There is a brown wire, a brown and white wire, a black wire, and a white wire running from the motor, a red wire running from the compressor, a yellow wire that runs from the compressor and connects to a little box inside the wiring panel and another yellow wire runs off the little box again. On the capacitor there are three sets of prongs that read "Fan", "C", and "Herm".

As of now, I have the brown wire and the brown and white wire both hooked to the prongs marked "Fan", the white wire hooked to the prong marked "Herm" along w/ the red wire from the compressor, the black wire hooked to the little box that the yellow wire is running to form the compressor, and the other yellow wire that runs from the little box is hooked to the prong marked "C". I'm not sure if this is correct or not, but when we turn everything on the fan and the compressor both work for a few minutes but then the fan stops running.

I was also wondering which direction the fan should be rotating. It is mounted w/ the fan blades and shaft from the motor facing down toward the compressor.

The Fan should be rotating so it blows air out the top. Swapping 2 wires can correct reverse rotation.

The brown and brown/white wire 1 goes to fan the other goes to c
The wiring instructions are/should be on the side of motor
If the capicitor wasn`t bad,you should leave old one alone leave compressor wire like they are and remove only the wires that went to old motor,a seporate much smaller capicitor was to be bought and used for the fan motor only,the motor lable tells what kind to buy