One of my interior doors has the top hinge with all the screws more or less
"floating in space". It has caused the door to sag a little. This seems
odd to me, since the other 2 hinges are solid as rocks, and yet there is
enough flex in a door somehow to bend or sag just "enough" to not close
perfectly.

Odd.

In *any* case, I am in need of understanding the *right* way a door should
have been hung: All the parts, what they're supposed to be screwed to, are
the hinge screws supposed to extend into the studs, what parts of the door
frame/jamb/whatever are connected to what.

No one I know is "sure", and I would like to know what /your/ opinion of a
good website or other source is.

I'm checking the other doors in the house, and am (I must be thick) now
wondering if this might worsen or outright /cause/ the strike-plate
repositioning I'm always going through.

--
Sometimes life just sucks, and then you live.