I have similar experience with Amazon support. It is fantastic when it falls within their defined parameters including refunding for purchases. But it appears that they don't have a system in place to actually listen to reader's problems and suggestions for features. It is very troubling because I had a small issue when sending my documents to Kindle via WiFi and the customer support only bounced back standard replies that didn't help at all. I gave up and asked Mobileread community for help and it solved my problem very quickly
Amazon apparently don't even keep a Knowledge base about bugs and issues of their own software.
As for having a Kindle with limited book purchasing rights, I guess you could make a separate Amazon account for your child and that account should not have a credit card on file. You can send books to this account as gifts bought from your own account. I recently gave a Kindle as a gift to a friend with some books preloaded. I registered this Kindle with a new account and it is possible to avoid leaving credit card for potential misuse in this new account while having Kindle fully registered and active.