Other Fuel System Pump problems of the 2016 Hyundai Elantra

When I attempt to start the car the engine turns but won't turn over. The car does this more often in very cold weather. Even in warm weather it will start sometimes and sometimes I have to try multiple times and sometimes it will not start at all. There are no check engine or other indicators that there is an issue with the car. The only other thing that may or may not be related that is different from what I normally expect is that sometimes the while driving, the car will not accelerate in a timely manner. There is a bit of a hesitation as if the fuel output is not increasing. This happens while I'm already driving (for example when I'm going from the access road and entering the highway or when there is a speed limit increase of some kind). I was told by a mechanic that the part affected is connected to other systems in the car that have an electrical component such as the fuel pump.