Thomas G. Marshall wrote:
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.

From your description it sounds to me like the screws have stripped out
of the wood jamb. Very simple fix. Remove the offending screws, dip
some toothpicks in glue and jam them into the oversize screw holes.
Cut off the toothpicks flush with the mortised jamb (called a hinge
gain) and reattach the hinge leaf with the old screws (assuming the
heads aren't stripped as well).

There's no need for the screws to extend into the jamb unless it's a
security door.

R