2003 Ford Explorer fuel gauge not true

That's common on any car when the fuel level is low. They have circuitry that prevents the gauge from jumping all over when you go around corners and up hills. That makes the remaining fuel wash away from the float on the sending unit, so it will read lower and take a while to come back up. When the car sits for a little while, the float remains steady and the reading will be more accurate.

Humming or buzzing is usually caused by a noisy wheel bearing, however, your vehicle doesn't use the design that is prone to developing this problem. Bad tire wear patterns can cause noises too but of all the wear problems, the one that causes noise will affect both front tires equally. An inspection at a tire and alignment shop will identify that. Ford has had real bad tire wear issues that can't be corrected since the early '80s, but that mainly affects their trucks and front-wheel-drive cars. The Explorer is one of their few vehicles that don't have this problem. Tire wear problems on yours will be due to worn parts and / or misalignment, not poor design.

Visit a tire store for an inspection. They'll be able to identify the cause of the noise.