U.S. Airforce Pilots: Is armed military aircraft allowed to fly over residential areas?

Yes - pilots overfly civilian areas going to/from training areas.  Look at the Tybee collision where a Mk.15 H-bomb was lost.

the US Military want a Permanent Base in Exmouth Australia because they can Fly at any Speed and Any Height day or Night taking off from the base over the sea

But Western Australia says No we dont want Americans in Australia and we dont need their money

Sure is allowed

Sure.  Any aircraft can fly over residential areas.

of course, its would be very hard, maybe impossible to not fly over rersidential areas

Kind of hard not to at many US Bases where residential areas have grown up around them.

What makes me chuckle are the fools that buy houses in those neighborhoods and then complain about the noise....