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Why exactly do you send a battle cruiser to search for your lost princess? Granted, it's given that the search started after the Graviton City extinction event and therefore also took 16 years. Best I can think of is that some of the planets they searched were hostile, and they added the weapons as they kept losing women.
Bear in mind that C-ko was lost to the alien empire when one of their battleships carrying her was damaged badly enough to crash on Earth in the first place. Given the size and power of those things, anything that could bring one down would probably be a considerable threat. They were simply being prudent in the search for their lost princess, not knowing what brought down her craft in the first place.
If A-ko really is the daughter of Superman and Wonder Woman, where are the rest of her powers?
Considering the series treats super powers somewhat realistically, this is simple DNA shuffling. There is a lot of fanfiction that gives her the rest of Dad's powers, but personally I think this takes away from what makes A-ko special. It also doesn't help that both Mom and Dad have pretty much the same powers, with only a few powers each particular to one or the other.
In Cinderella Rhapsody, the dub anyway, is A-ko breaking the fourth wall when she thinks to the audience "so I fibbed a little"? She does seem to face the "camera" in that scene. Her dream/hallucination in Vs. is a clearer breaking of the fourth wall.
Does A-ko wear wrist bands when she goes swimming or not? On the Collector's Edition, there are scenes wear she appears to be wearing mini wrist bands and others where her forearms are indisputably bare.