Does this power work ON TOP of the earth or INSIDE the earth? Or both?

Generally speaking, it works anywhere. That said, it doesn't allow the elemental to push things through the earth, generally speaking. Tunneling is a fairly trivial service for most earth elementals, but that's not movement per se.

Just to make sure we are all in understanding, earth elementals can use their power to speed up or slow down creatures that are in contact with solid ground, be they moving along the surface or tunneling through it. The movement power does not grant the elemental, or those affected by the power, any special ability to move through solid ground.

I wonder how this would effect someone who called an elemental to use this power to tunnel through the earth while astrally projecting.

Movement, being a physical power, doesn't affect the astral plane at all.

I also don't know whether or not it'd help someone tunneling... if whatever your method of moving the earth aside isn't moving much faster than you're already moving, then you'd be in trouble.

Well, really, if you want to start applying "logic" to this, I dont really see any way an earth elemental could make you run faster. But it can. Its magic. I dont have any problem saying it can help you tunnel faster.

Who says you are running faster? Your speed in relation to the ground can remain Qx(running multiplier)+(result of athletics successes), just that the specific ground involved is also moving in relation to the surroundings.

You know... I've tried to form a mental picture of that happening... and I just cant. But whatever. If the movement power can cause a localized patch of solid rock to move such that your end speed is 5 times faster than it otherwise would be (in the case of a force 5 spirit), it can *certainly* make it easier to tunnel through dirt.