Is it possible to view files stored in iCloud Backup? I have a backup for my iPhone 5s from January. Is there any way I can download them onto my computer ? 



Is there any way I can look into the files that were backed up onto iCloud?
No and no, I'm afraid,

You could restore the iCloud backup to the device, then back it up to the computer and use a 3rd party tool to dig into that backup file, but you won't be able to get at the iCloud backup contents directly.