First before anything else, change the oil! Gas contaminated oil will spell disaster for these engines. Refill with a quality brand oil, 10w-30. Since this engine takes just over a quart, no reason not to spend the extra couple bucks on synthetic.
There should be no fuel present in the line that runs to the engine crankcase. If there is, the pump is done and needs replacement. If there is oil in this line, the pump has probably been contaminated and needs replacement. Start with a replacement pump, this one works nicely on my 625:
https://www.amazon.com/Walbro-FPC-1-...s%2C186&sr=8-5
Ensure all lines are run properly, the pump has arrows and letters for the different lines. Arrow pointing towards the pump is the fuel inlet from tank. Arrow pointing away from the pump is the fuel outlet to the carb. P stands for pulse and is the line that connects to your engine crankcase.
When that is all hooked up correctly, try running the engine. Some carb tuning will be necessary, as it is very unlikely to run well out of the box. First step is to get idle set, and a tachometer is highly recommended. Idle needs to be low enough to allow the cart to shift but high enough to keep from stalling. Once the idle is set, then you can work on carb adjustment through the rpm range. Again, an adjustable main jet is highly recommended for this step. It will make your life much easier. Try this one from NR racing:
http://www.nrracing.com/product-p/99101-zh8-ajust.htm
If you are getting fouled plugs, and the engine is dying out at higher rpm try turning the adjustable jet in to restrict the amount of fuel the engine is getting. If your plugs are white or the electrode has black speckles on it turn the adjustable jet out to allow more fuel into the engine.
Lastly, I recommend installing a fuel return line. This line tees out of the fuel supply line from the pump to the carb and allows excess fuel to return to the tank. Some may not need to do this, but its cheap insurance against an engine that isn't running quite right. Here is an example of what I have done. The picture shows my engine bay with clear fuel line. My engine would flood the carb before I performed this last step, and with a good pulse signal and a quality pump it is likely to happen to you.