The ability to block websites is typically done with a web proxy (which may be difficult for her to setup and administer). If you're interested, look into squid and squidguard or Dan's Guardian.
Now there is a simple way to do it provided the kids don't have access to the /etc/hosts file (which if the kids use sudo, you'll have to edit the sudoers file to prevent access to /etc/hosts, if they don't have sudo access, then no problem because they can't edit the file). Basically, what you do is point myspace back to localhost, so the page can't load (DNS always checks your hosts file before trying to contact a DNS server). Here's a link
describing it further and it has some links to fairly comprehensive hosts files blocking any number of things.
As for Gaim, I don't know, but if she knows where the logs are, she should be able to read them by sudo more logfile
since that will give her root access to their home directories.
iTunes, I don't know what to do about. Although a friend of mine found a script to convert all the m4a files to mp3 files, which also play on iPods. I believe he just transfered files by plugging the drive in and mounting it as a USB stick. Then opening konqueror and copy and pasting files. Don't have an ipod, so I'm not much help...
Just did a bit of googling, seems there's a library or plugin called "faad" that might help you play m4a files in Rhythmbox