No (read Updates).
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Can an Elite Spellcaster turn the 4 from the tinge roll to 3 to avoid receiving tinge?
No (read Updates).
Does a unit with the keyword Cover benefit from it, or only the adjacent units?
Only the adjacent units.
If a Scout unit deploys at the start of the game, can it move or attack?
No, if it deploys at the start of the game it simply sets up on the battlefield following its special deployment conditions.
Can I perform a non-move action when I activate and deploy with my Scout unit?
Yes. When you deploy as Scout once the game has started, you may perform a single simple action (activating a skill, casting a spell, etc.).
Scout / Ambusher
If during deployment you already have a unit on the battlefield and you decide to deploy a Character with the keyword Scout to lead the unit, do you get to take advantage of the Scout rule to re-deploy the Hunters at the end of the deployment phase?
No, if a unit is already deployed it cannot be redeployed. If you want to join a Character to a unit (so that it gains the keyword Scout/Ambusher by effect of a skill), leave both off the battlefield and place the Character's profile card under the unit's. When the unit deploys, the Character must deploy as part of it.