I have a 91 honda civic base model hatch with a d15 I have changed the fuel pump in the gas tank and fuel relay I have also checked my hoses on the motor theres no cuts and there all connected.
My car starts but when I accelerate it turns off and it turned off on me when I was driving.

 

With the car running, try just jiggling the key in the ignition.. sometimes these old ignition plugs tend to go bad and cut out like you turned your key off. It's not the lock itself but the white plastic plug that connects to the back of it that makes the connection when turned. They are easy to change, a few screws and a plug from the harness..

 

My car turns on fine but when I put it in gear is when it turns off

 

Is your tank full or partially filled?

When you replaced the pump, did you re-use the OEM sock or did you use the sock that came with the pump? Nearly all aftermarket pumps (even good brands like Walbro) come with a sock that does not mount horizontally in the bottom of the tank. If you use the sock that comes with the pump, it will allow the pump to start drawing in air when you get down to a partial tank (about half tank), which could lead to not enough fuel being delivered. This may become more exaggerated due to sloshing or being on a hill, and could cause the car to shut off.

 

I just removed the fuel tank drain plug air pushed out and no gas drained from it at all but when it last turned off on me it marked that I still had fuel so I think it's the fuel pump unit.
what fuel pump unit would you recommend

 

Left is the original right is the one i just took out