Zanscare have at least some underage cadets working together with regular soldiers on battleships and even doing active piloting. Uso met a girl about his age on one of the bike-ships, and saw her killed by "friendly" fire.
Adding to your point, Katejina was 17 when she fought for the Zanscare. I don't remember Chronicle's age, but I believe it was about the same.
And to keep the topic on Haman, was it ever stated how exactly she rose to power among the Axis Zeon?