I'm using avira and I just backed-up my system. I plan to format my hard drive and before restoring it, I'd like to scan the backup file (.bkf) just to make sure that my pc's really really clean. Will it be able to detect if the backup file has viruses?

In the same sense, how about spyware, will antispyware tools detect spyware inside a backup file?

thanks

Yes they will check for Virus inside an archive, but in standard (default) condition they will check 3 layers down. You can set them (in advanced options) to more levels down, but normally this is not needed.
Suffice to say, that they are checked
Not only that, but when you then open them (or load the backup back up!) the file will be scanned again, so not to worry about this.