2006 S500 W221 A273

Question

Hie
Ive got a 2006 S500 W221 A273 MERCEDES it started off hard cranking in the morning then it would start. Drive for about an hour to town get to the traffic lights and I could feel like a misfire. Park for about 20 mins or so get back into the car try crank and it will start and die. If I'm lucky it will start on the 3rd go or wait an hour and she'll surely start. Sometimes though not so often. Right I got a fuel pump from a mate and I'm not 100% comfortable with fitting it because I noticed that when the car didn't start the day I planned to install the new pump I had no current coming to the fuel pump socket thinking of checking the other side but it seems to have only one pump and nothing but a plastic sender unit I presume. Checked all the fuses related to the fuel pump all ok. Try crank again pump starts pumping again drive out acceleration normal I suppose still can feel misfire. (Pump returnable if seal unbroken) . Please help