...since this "inverting salectedness" makes many actions impossible, because there's no way to get simply the opposite selection form what one have achieved (there's no way to control/find out if the currently-selected pixel will be "inverted" selection). Reproducible: Always
There is only one to invert. So I guess what you want want is to have a 0/1 selected/unselected selection.
Yup. I don't know the exact mechanics behind the current inversion, but I think it shouldn't be much work to enable such 0/1 option, since even with this "selectedness" there's always some selection border drawn - so easiest way is just to treat the interior as 1 and everything else as 0.
You can just disable anti-aliasing in the selection tools.
That works nice with all but "select opaque" - there's no possibility to disable it there, since it's automatic selection.