IPhone / iPod music problem

Yes. When you have the device plugged in, click on its icon in the navigation bar on the right, then in the main part of the window turn on manual management for the various types of content as shown across the top of the window.

It is, however, a very good idea to have some kind of a back up of your iDevice's content somewhere in case something bad happens with the device. External Firewire and USB hard drives can be had very extremely cheap.

Plug her phone back into iTunes. In iTunes, click on her iphone, and in Options uncheck anything having to do with "Syncing Automatically". If it's not already checked, click "Manually manage music and videos".

If you want her to have a separate iTunes library, she should also have a separate login for the shared computer. This is really the easiest way to deal anything on a shared computer.

Incidentally, there shouldn't really be any reason to physically plug your iPhone into your computer anymore. You can actually set the phone (and iPads, etc) to sync wirelessly.