Hello and Welcome here Eve,
AFAIK, Nero is compatible with windows 98SE, so you shouldn't worry to buy it. It's a great drive
Concerning uninstallation of previous driver for your cd-rom, Windows should handle all of this correctly. There's no need to remove anything (you can even keep your CD-ROM drive if you wish). Finally, a backup is not required, but if you are unsure, then go for it.
Hope I answer your questions,