Firefox (Safe Mode) is a shortcut link in the Start Menu > All Programs listing in the Firefox browser. You can easily just delete that shortcut, right click that entry and select delete. That removes the shortcut from the Start menu but any person with the knowledge or the will to do a bit of searching. Here's some of the problems;

1] That shortcut points to "C:\Program Files\Mozilla Firefox\firefox.exe" -safe-mode" which is in the Program Files folder on the hard drive.

A user can simply create a new shortcut from that 'firefox.exe' file, (right click the file, select either "Send to" or "Create Shortcut"), and in the Shortcut Properties, right click the shortcut icon, select Properties), can change the target entry from "firefox.exe" to "firefox.exe -safe-mode". Place that shortcut on the Desktop, or anywhere else the user likes out of view of others, and they can use it whenever they want.

2] Even if they do not create that new shortcut, they can use the Command Prompt "Run" command firefox.exe -safe-mode and Firefox will open in it's Safe Mode.

If the Start menu does not show the Run link, the user can use Search to search for Run, and carry on from there.

So, preventing the user from using Firefox in it's Safe Mode is difficult in an Admin capable Windows account. The confident user can always find a way around it.

3] Private Browsing is a new feature in Firefox and can be turned on or off from the Firefox Tools menu. There's more about the feature here;

So, anyone can turn it off, or back on.

4] Firefox did not make a 'one-push-button' option to permanently disable Private Browsing. However, there is a way, but it needs work by you. The guidance is here;

What I think;

I am unsure why Firefox was being used in it's Safe Mode. That is a diagnostic mode for diagnosing problems with the browser and if the user found out that using Firefox in this way disabled Norton's Parental Control components, then this suggests a sophisticated and knowledgeable user. That is a difficult situation to control, especially since you yourself say you are not computer savy.

I would ask a question. Does this user log on to Windows with an Admin capable account? If so I would change that. This is what I would do;

a) Make sure your own Admin capable account is password protected. No simple passwords, (eg dates of birth, family names, name of dog, cat, etc), something that is longer than 8 characters and cannot be known or guessed by this user. Do NOT forget your own password

b) If the account you are using is one you created yourself, make sure the hidden System Administrator account is also passworded.

c) Create a new, Limited User account for this user.

d) Delete the user's existing Admin capable account. Note, any software this user installed themselves will also be deleted, as will any personal files, documents, pictures, music, videos, etc, so make sure they are backed up beforehand.

You mentioned problems with IE. May be they should be solved as well?

Sorry, none of this is going to be easy, and much of it can be circumvented by a person with knowledge.