can I delete the older versions of Photoshop I have (Photoshop 7) or will that make it so I cannot use CS3 since it was only an upgrade?
#1
The upgrade is a full installer. It does not need any components from a prior version. If it doesn't find a pre-existing version to read the serial number, it will prompt the user for the old serial number as well as the new one.
Yes, you can delete the older version if you want.
#2