I've Norton Family installed on my son's computer, which has Windows 7 64-bit. The settings indicate that Noton should be alerting me when he attempts to visit a blocked sight, but it doesn't. It seems to think he hasn't been on the Internet for the last seven days.
Also, it is supposed to be set up to block harmful search content. It doesn't. I tested it and found that a search on Google with the right key words would turn up all kinds of stuff no parent would want their kids to see.
If there's a fix, I'd like to know, but really, making parents think that you are helping them block this kind of stuff when you clearly aren't does a whole lot more harm then good.
From what you described, it almost sounds like none of the functions works, then it's very possible that Norton Family is not installed properly or the child's account is not associated with his/her Windows account correctly.
Please check out the links below on how to associate Windows accounts for Norton Family.