The gas gauge is separate. When you take the dash panel off, it just surrounds the gas gauge and the gauge stays on the tank. That way you can get to the ignition switch, the speedometer, the dash light and the ammeter without disturbing the gas gauge. The gas tank gauge requires an empty tank and a special tool to remove the chrome rosette surrounding the gauge.
You are correct that the float and indicator are mechanical. There is nothing electrical about that gauge.
If it isn't leaking or if it registers reasonably, and if you have no real reason to remove the gas gauge, I would advise against messing with that.
The other parts are easy. 4 screws, like others have said.