Sending Unit bad?
Bend the float rod down. Youll see a full tank but may never see empty.....;-) I dont think a dent would affect the sender.
Sure it will, depending on the size. A dent in the bottom moves a certain volume of gas higher up compared to the swing of the float arm (in other words, the float is floating higher compared to the actual volume of liquid). But it should make the gauge read higher, not low -- the dent is taking up space that would otherwise be occupied by gas.
You might want to test it by running the tank completely empty, then seeing how much gas you can fit in before it kicks off, noting at what point the fuel gauge stops going up. I realize that's a hassle...
If you don't know where the dent came from, here's something to think about: I once had the fuel tank "implode" -- it basically sucked itself flat. The circumstances were: 1) the vent pipe was clogged (unbeknownst to me), 2) I ran the tank down below 1/4 on a very hot day, 3) I parked the car overnight at high altitude, and (4) the temp dropped into the 40s. All the vapor in the tank condensed into liquid, creating an instant vacuum. I was confused the next morning when the gauge read over 1/2, then when I stopped at the gas station, I could only put in 2 gallons. This made me look underneath. Oops.