Re: how to back up MS OneNote to iCloud?
I'm not sure that you can do this. Even if you can, I'm not sure that you should. OneNote is designed so that your information is available on whatever device you might be using (iPhone, iPad, Mac, Windows pc, Android device, etc). Backing up your OneNote files to iCloud instead of OneDrive would remove that convenience.
That being said, I'm pretty sure that you can save files from OneNote to iCloud Drive. Make sure that OneNote switch is turned on in iCloud Drive settings on your iPhone.