Multiple fuel issues, possibly same problem

[ZeroTolerenz]

I have a 1988 Mustang 2.3 4cyl engine. I am not sure, but possibly my low battery power could be the problem, seeing as I have an electric fuel pump. I use a good bit of fuel injector cleaner, so I know that clogged fuel injectors probably aren't the problem. About a year ago, my car just died, acting as if I had run out of gas, but I just filled it up. I waited a couple of days, left it sitting where it broke down, and I changed the fuel filter. It started right back up with no problem. 6 months later, the same thing happened, but I changed the fuel filter immediately, but it still would not start. I left it there for 2 days, and it started up like nothing happened. Now, I was informed that it was the fuel pump, but if the fuel pump went out, then would it not start back at all? Also, my fuel guage quit working correctly around the time that this had first happened; it will go all the way to the full mark when I rev it up. Also, sometimes when I pump gas, the nozzle will act as if I had a full tank, you know, "click" or what not. Could all of these issues contain the same problem? They say that it will cost me over $300 to replace the fuel pump, because it is in my tank. I dont want to pay that kind of money if it is not the fuel pump, and they want $30-$60 to check my fuel system to find the problem. I am not sure if it is the catalitic converter, but there is a hole the size of a silver dollar an inch before it. The acceleration has always sucked somewhat unless it is warmed up for about 15 or so minutes, even in the summer. It is not the transmission fluid. What could the problem be?