An AAV is a one-way air valve...it will let air in only (if it is working properly). If it is already up in the attic, the best choice would be to put a T on the existing vent going through the roof, and connect that one to it. You might need to upgrade the size of the pipe going through the roof. Condensation is probably normal, as the air is humid in the vents and the attic this time of year is likely cold.
A whole-house p-trap isn't necessary, and could be a source of hassles in the future.