I have a 1TB external USB hard-drive.
When I first got it and installed it, the first thing I did was re-format it (not saying everyone should do this, it's just somehing I like to do) so I have a perfectly blank canvas for XP to interface with using XP settings.
By doing this, Explorer recognises the new hard drive easily and now I simply drag & drop into it via explorer, create folders, download directly into it (legally, of course
).
The reason you're not prompted to back-up to it is probably because your operating system either does not recognise it or you haven't configured your settings for it.
It's like when you use WMP and want to check your library - unless you nominate that drive in WMP settings it won't know to look there for any files.
As far as your CDRW not reading CD's - get a new one. You should not be having this much trouble with brand new blank CD's (irrespective of the brand). Upgrade to a new DVD so you can burn CD's and DVD's - they're pretty cheap these days.