Yes. Note that you cannot use the ability in-between movement points. For example, if a unit with Movement 2 uses a combinable ability, it cannot move 1 hex, use the ability, and then move another hex.
Shields are a form of damage reduction. Pure damage ignores all damage reduction effects. When unit receives pure damage, you would deal that much damage to the unit and, if it is still alive, it will have the same amount of shield that it had before combat started.
No. Ability levels are not considered part of the ability name. Therefore, Quicken 1 and Quicken 2 are both considered the same ability and the “Use this ability only once per round” restriction applies.