From what you describe, the flue is obviously to open the chimney. The switch for the motor sounds like a fan to circulate air that's warmed by the fireplace and push it back into the room. The Open / Close lever sounds like a draft control so that you don't get a wind tunnel effect through the doors. On mine, this lever allows fresh air from outside to come in under the fire, thus preventing the fire from pulling all of its air from inside the house. This prevents your house from getting chilled, causing the thermostat to compensate for all the warm air lost up the chimney.

On 1, that is how mine works. A spring pushes it open--you have to pull down on the cable to lower the damper and keep it under tension to close it. On 2, I don't know for sure. The experience with mine is that there seems to be some amount of air infiltration when closed, but not much.

Do you have UL Listings?

If your fireplace unit and your surround were installed and constructed following the UL and building code standards, you can certainly paint the remaining enclosing finish material. Depending on the type of installation you have, you must have incombustible material for a specified distance around all sides of the fireplace opening, and you must have an incombustible hearth for a specified distance beneath the opening. Sounds like you need to check with your local building official.