Backing up on a FAT32 drive is probably not the best idea, there are limitations and the journaling does not work properly. I would seriously consider re-formatting your external drive to NTFS, which would make these incompatibilities go away.
Also, Windows backup is not as reliable or fast as some 3rd party backup solutions, I would also recommend Googling 'top 10 free backup software' and read a bit till you find one that is right for you.
Doing a clean install will not make these problems go away. Though the recovery disks not being recognized is a major issue and you should definitely make more if those ones don't work. They may do though, you actually have to boot from them to make them work. You can change your boot order in the Bios which you will find by pressing f2 or f8 or whatever your computer asks when your machine is booting... then change boot order to cd first rather than hd and restart the machine with the first disk inserted. Doing this will not make your current issues go away though.
Hope this helps