You can verify a Flash *should* be good by plugging Audrey in with the Datebook button held. It'll read the Flash, then boot, and if you don't receive an error, then you should be in business. The screen will flicker after Audrey is started up by this method... this is normal. Remove the CF from Audrey before shutting her back down.
As for your second question, you can make backups of Audrey without using a CF across a network to a mounted drive. However, the caveat is that in order to use them, you need to get them back onto a CF to boot Audrey from. If she is still in good working order, this can be done back through the mount. If she is dead, you'll need to get them onto a CF from your computer. This can be accomplished in a variety of ways using either the ntrw utility or by using Gemexporer (which I can't get to work with Win 2000 or XP).
Any which way you go, you'll need a compact flash eventually. I'd suggest getting the Sandisk 32mb as people have had problems with some other brands and sizes. In theory anything over 16MB should work, but it doesn't hurt to stick to the Sandisk 32mb on this item as it could save you a lot of headaches down the road.
I haven't heard/read of anybody getting the serial port working as a flash method yet although there seems to be some interest (for those times that the CF socket dies). I'm not willing to fry my audrey by testing sending an image to her over this method though. If she was already dead (and could not be recovered by CF), then I'd be open for experimentation, as I'm sure some others will eventually be.
The other images are replacements of sorts. They are actually customized factory images. Due to flash memory constraints though, when you add something to Audrey, you invariably have to look at removing something else. So look at the specifications of each image, since some may have removed things you'd like to keep. Most people find Audrey in her original image form fairly constraining and want added features (home automation, streaming music, etc). Have fun.