Can anyone help me find out what's under the drilled cover in this picture (right in front of the rear axle). I guess therre's a braided hose or two going in there, and whatever it is is missing on my car.

 

well for starter looks like you're missing some exhaust piping .. secondly if you're taking about the piece thats in the center right of that picture ... thats where the fuel pump normally is

 

Thanks for the info.

That's not actually my car. My car is standing 100 miles away.

Does the fuel pump have braided rubber hoses or metal fuel lines going to it?

 

Steel until they get to the pump, then rubber to make the connection.(stock) If they are braided hoses then someone has changed them.

 

someone might of went with an after market system which is not uncommon

 

According to the factory manual, there are supposed to be two valves, a check valve and an out valve. Do I need either of those to run the car, or can I simplify the system to be just the fuel pump?

 

those valves are in there for safety purposes. The check valve is so that the fuel doesn't flow backwards and the cut off valve is incase a fire arises, the cut off valve would stop the supply of fuel from the tank. Having said that ... you can still do it the other way ... but not really recommended unless you go with an aftermarket fuel cutoff safety system.