I'm not sure if there is a minimum age for a child to have charging privileges but I know I was able to allow my 10-yo to have charging privileges last year. That being said, she didn't know she had charging privileges. I did it just in case we switched magic bands so she could use a FP on mine. I wanted to be able to purchase a snack or drink or something in a gift shop while waiting for her to ride the attraction. If you give a child charging privileges, they will need to know the PIN code to make any charges -- so I always assign charging privileges to all of our magic bands, I just don't tell the kids the PIN code until/unless they need to use it.
As far as I know, while it is possible to attach a specific credit card to a specific magic band, I don't think it's possible to assign a gift card to a certain person/magic band. A gift card can be used to pay down the balance on a room charge or it can be used for the actual purchases, but I haven't heard/read of anyone being able to assign one to a specific magic band or apply it towards specific line-item room charges. Some CM's seem to be willing/able to apply gift cards to the room charge even when there is no balance to be paid down (so, giving the room charge a "negative balance"), but that varies by CM and seems to be the exception rather than the rule. It doesn't hurt to ask at check-in, but be prepared with a back-up plan. FWIW, the room charge print-out will list each individual charge and who made the charge so if you're simply trying to keep track of charges by person, you can just ask for a printout of the room charges and add them up by person.