Fuel pressure

I recently got this car after it had been sitting for awhile. I did a complete tune up. I noticed though that the fuel guage did not work. I have been putting fuel cleaner in the system to clean it out. The fuel sending unit seems to be working now, but im wondering if I have a problem with my fuel pump?

At low speeds from 30 and under the car has been hesitating, and even stalling. I drove the car, over 500 miles to see if I could burn out all the junk that was in the gas tank, and I was fine most of the way until I got off an exit near the end of the trip and it started hesitating uphill and then eventually stalling.

It does not happen at high speeds, but at the light, or low speed and even trying to go up hill, the engine stalls and dies or acts erractic, yet it doesnt die all the time or happen everytime im at low speed!

So I have already replaced the fuel filter, and have been using fuel cleaner, but even if I was able to travel a long distance is the problem still the fuel pump?

I say the fuel pump because I know that the fuel pump and fuel sending unit are together, and as I mentioned earlier, the fuel sending unit had been having problems.

So is it the fuel pump or am I missing something else? What else could it be? Fyi, it has a new battery, spark plugs, spark plug wires, hoses, air filter, fuel filter.