Questions regarding magnets?

Andrew has a good answer but to add a couple comments...

On storing in a vacuum... it depends. In the vacuum of space, things that are exposed to the sun's light get quite hot. All permanent magnet materials have a Curie Temperature. If you heat it to above the Curie Temperature, it loses its permanent magnetism. You can restore it by remagnetizing once it cools down.

As another answer suggests... unless it is stored at absolute zero, there is some thermal energy which will tend to increase entropy and degrade the magnetic domains. This is why most permanent magnets are sold with a "keeper", a piece of metal that has very high magnetic permeability and, therefore, concentrates the magnetic field across the N/S poles and helps maintain field strength (at least it does if it is in place when the magnet is stored).

As far as falling??? It depends. You may be able to test this yourself. Get a powerful permanent magnet, NdFeB. Get a piece of Al the same size (does not need to be the same mass). Then get a couple different tubes to drop these thru, say some plastic pipe, a cardboard tube, a length of copper pipe, try different things. Ideally, the tubes should be just a little bigger diameter than the magnet/Al piece. Now observe what happens when you drop the Al vs the magnet.

If there are differences, would they be due to gravity or something else?

1. Yes. Space will not affect a magnet.

2. Possibly forever. Although given the kinetic model there is a small possibility that some molecules have sufficient energy to disrupt the alignment of a magnetic domain so over a long enough period of time the magnet MAY lose some of its strength.

3. The magnetic forces on a magnet in the earth's field are almost non existent.

Because any forces on the North end are exactly countered by the reverse forces on the South end unless the magnet is in a field with differential strength or direction.

As the earth is so large then there is no significant difference in the magnetic field of the earth at each end of the falling bar magnet.

Depends on wheter it is a shop vac or a standard househole vac. Once it looses it's magnetic properties it is no longer a magnet so techincly the answer would be forever. Yes, especialy if it's attached to a car. Even more so if it's attached to a jet propeled rocket.