Legal working age of 15 1/2 (in my state) plus a kid who looks young for their age - may not be the most appealing situation, bit this probably completely above board.
No age restrictions if family owned business, that's a federal law no state can bypass, but I doubt the owner of Culver's needs their kids to work to support the family.
That's a federal law aimed at farm families from back in the day. And farm kids are still helping and working along side Grandpa and Dad. And where I live, in the middle of a forest, they also help and work along side in logging families also.
Growing up on a farm, my earliest memory in life is walking behind a tractor pulling a 'stoneboat' and picking up rocks in the fields along side my father and grandfather. I was driving a tractor pulling wagons and hay trailers by 8 years old and by 12 I was driving trucks hauling grain from the field to storage bins and unloading them. Plus getting up a 5AM to help milk cows every morning and again at 5PM. It was absolutely crucial when my Grandfather got sick with "Farmer's Lung" and couldn't work much anymore. I pretty much started running his farm at 14.