No, a stalling problem like this will not (cannot) be caused by a horizontal fuel filter.
No, you do not need (and really do not want) to go adding electric fuel pumps. You're not having this problem because the car doesn't have an electric fuel pump; once you find and fix the problem it will go away.
Two items not yet mentioned: the rubber hose from the hard line to the inlet of the fuel pump, and the strainer on the end of the fuel pickup pipe inside the tank (part of the sender): new, old, absent?