When the fuel level in my car comes to the red zone I feel the running more heavy, the car needs more throttle and is more difficult to gain speed. Is this something normal??
The fuel tank might be dirty, causing issues with the fuel pump picking up enough fuel.
Also, some vehicles don't like been driven on empty tanks and this can often result in poor performance or stuttering as you attempt to accelerate.
I'd have the fuel tank removed and cleaned. I would also replace fuel filters for good measure.