Can you move a land claim, e.g. "unclaim" a piece of land you have and claim another piece instead?

You can't unclaim a property and switch it for another, but you can sell your property back to the UEE, a property broker or another player at an agreed or present market value. If you bought a dry patch of desert and struck gold but don't want to bother with the excavation - or the security hassles of guarding it - you could likely sell it for a profit. If, on the other hand, you're just looking to dump a worthless plot of land back on the original seller you're likely going to take a pretty good hit.