Several Parakeet Questions. Please Help me!?

Your birds are beautiful! Light will trigger mating even if it's just a lamp but all birds need 12 hours of darkness for their health. The more hours of light they get will advance their mating desire. The males iris will get bigger when he is ready to mate & mine have never shown an interest in their nest box except to chew on the top of it. Your female apparently is not old enough yet for babies & you don't need special perches. There is nothing you can do to help mother nature with the breeding process. They will do what birds do when the time is right.