Yeah, the ages are whack even by anime standards.
Yuuno getting authorization is unique to this manga version; in the series he was just on some expedition, and the survivor after the ship failed (or was attacked by Precia?) Of course that's odd too, but "orphan in some tribe" handwave.
Nanoha's "what do I do my life" angst seems more appropriate for at least 12, if not older, not 9.
(Also she's 9 at the beginning of 3rd grade, which is weird in a totally different way. Should be 8, or should be 4th grade.)
Amy is 16 and she's not even an obvious mage, let alone a human-WMD one. You can imagine that precocious WMDs at least need to be given social structure so they don't go off on their own, also they're useful.
On the flip side, the modern length of 'childhood' is historically unusual, and perhaps not necessary. Perhaps Midchilda is more into apprenticeships and part-time formal education rather than keeping teens out of the work force.