Good questions. Moving cars may vary with the era?
Sidings way back may have been designed with a slope to use gravity?
I once worked for an warehouse operation in Denver where we just used
a flatbed truck like a local lumber delivery would use to move fully loaded
boxcars around as needed pulling with a tow chain. Level track but the
cars moved easily and we used the RR brake wheel for control.
Once at the crrm long ago, a famous jeeper used his winch to move the
20, we also used pinch bars under the wheels to move a few things around
but that is slow going unless there is a downgrade.
I would think a small hand winch could move a car (I have a 3 ton), or horses,
or a tractor. The mines use air winches to move stuff around underground
and they would work anywhere there is air or steam but have no idea when
they appeared.
The modern coal loading into RR cars east of me is done from above and
RR crews move the complete train as needed according the miners I've
talked to. They load the whole train until done.
Maybe not the right answer but you don't always need a locomotive.