I don't know of a way to prevent your Aunt from deleting the password. You could set the computer up so that every time she restarts the PC is always goes back to the settings you created. That way she couldn't accidentally permanently change or accidentally delete anything that she shouldn't. That's how I set the PC's up at work and I wish I could do that to home users, too.
You can set the computer up to connect automatically when she click on the e for internet explorer, but I don't know that this would be a good idea. She could accidentally install a program that has the ability to connect itself to the internet and with the settings on automatic it could do so. The caveat is that it won't automatically disconnect and then her phone line would be tied up and she wouldn't know why.