Theoretically, money spent in a distant futures contract, would not be receiving interests, as if it were invested in bonds. So, using by-the-book definition, what is the normal state in currency futures: Contango or Backwardation?
Depends on the relative interest rates of the underlying pair. If the cash pair is interest bearing, then the future will be in contango to account for the foregone interest.
No, +swap fx futures trade at a discount to spot, not contango. This backwardation is analogous to the discount on a zero-coupon bond. There is no interest payment made, so the contract must trade at a discount to spot. EuroFX futures trade at a discount to spot EURUSD.