It sounds like its time for a visit back to your dealership.
You're correct: using the city water connection should not fill your fresh water tank. Have your dealer take a look at the system.
The drain plug is located on the bottom of the fresh water tank, close to the middle of the trailer. Simply unscrew the plug to release the water. Your fresh water tank is white in colour, as opposed to black in colour for the grey and black tanks.
As far as your grey tank filling when you flush the toilet, its possible that your tank sensors were wired incorrectly (i.e. the black tank sensors were wired to the grey lights on the control panel). Again, your dealer will be able to correct this for you.
Good luck!