Q: Gas gauge & pumping gas

Hello, It sounds like you may have two separate issues going on here. Your car has a float type device inside he fuel tank which measures the level of the fuel and sends a signal to the computer which then registers this on your fuel gauge indicating how much fuel is left in the tank. This is called a fuel sending unit. With respect to pumping fuel into the tank, you may have a faulty purge valve solenoid which is a component in your evaporative emissions control system that controls the venting of fuel vapors from the tank and diverts them to a charcoal canister that is designed to absorb them until they are released back into the fuel system and then burned with the rest of the fuel. When this is not working properly, you may experience the gas pump shutting off prematurely causing it to take a very long time to fill up your fuel tank. This is due to the excess fuel vapor that is present when the purge solenoid is not working properly by releasing these vapors. The gas pumps at the fuel station have automatic sensors on them (for safety reasons) that shut off automatically when too much fuel vapor is present. I would recommend having an expert from Your Mechanic come to your home to take a look at your car to diagnose your EVAP purge solenoid.