You need to check fuel pressure to verify if system is building enough pressure. Remember the fuel pump only runs momentarily to charge the system then comes back on once engine starts. Below see test procedure.
Also check all connection at pump and pass through on sending unit for any signs of heat build up.
The 3 wires to your sending unit purple is fuel level signal to cluster,gray power to fuel pump, black/white ground. Below is the basic circuit for the fuel pump relay. the Ecm controls the relay and the ecm b fuse supplies voltage to relay. Find the fuel pump test lead and apply battery voltage to it and see if the pump runs.
As far as regulator do you have a tbi system or cpi system if your not sure then get me the 8th digit of vin it will either be a w (cpi) or z (tbi)
Voltage goes from the relay to a splice that connects wires from the fuel pump, ecm, oil pressure switch. I have seen alot of problems where the wires go through the sending unit inspect it closely for and darking as signs of heat build up.