If I double twice, is it multiplied by 4?
Yes.
What happens if the striking unit and the unit-being-struck are at different locations (e.g. from a unit with the Ranged ability, or Quarrelsome Kobolds)?
The strike occurs at the location of the unit being struck. If the unit being struck is nearby the Mask, they will take double damage.
My minion starts nearby the Mask and thus must attack. During my Move and Attack mandatory action, my minion moves so that it's no longer near the Mask. Do I still have to attack?
No, since you do not actually attack until after moving. If your minion is no longer nearby the Mask, you are not required to attack after moving.
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