All knives or just Switchblades and gravity knives
I carried a knife from about 4th grade on, as did most kids including many girls. I suppose I had "permission" but it's not like I had a notarized letter to carry around.
Only switchblades and gravity knives, not any other kind of knife. in that they are treated like firearms. Which is "meh" but whatcha gonna do? And the possession doesn't require proof of prior written permission, the parents or legal guardian would eliminate any charge by saying "yeah, I gave her permission." But you can't stop someone in Alaska to check their knife, even a minor, there'd have to be some other reason for the question to arise in the first place.
The sale or transfer requiring prior written permission is something the vendor has to verify, like buying booze, cigarettes, or guns. Kid has switchblade, says they bought it from Bob's Knives or their buddy Steve gave it to them, Bob and Steve better have a written record of the permission to buy/transfer.
Possession only requires parental approval -under- 16, and is perfectly legal from 16-18. A 16-18 year old asked by a cop where they got a switchblade is under no legal obligation to tell them. If the cop didn't see the transaction they can't do anything.