The rule that you get a unique racial move card seems to confuse new players often enough that it would probably be worth the effort to make unique cards for them. Something like Dwarven/Human/Elven move?
That's... a really good idea. And so simple! I'm surprised it hasn't been suggested before (apologies if it has, I've not seen it).
Dwarven Amble? Human Movement X? Elven Spurt? Not sure this is needed (although I agree that some people fail to grasp it being a potential issue), and would be weird if monster decks kept drawing the regular ones - they use a racial mechanic for movement cards as well.
I'm not sure I like the Elven Spurt name, sounds like a dodgy LotR movie I once saw. I mean my friend did. And not me. No, not me.
Good idea. Doesn't have to be the name of the card, just the origin, like "Pentrating Stab" comes from "Dagger". This "Run" comes from "[Human Movement]".