Where do the noted that are saved on the Note application disappear to?
Probably to your email. The Notes folder. If you turned off that email in the notes app, the notes go to that email address to the Notes Folder. But to see the Notes folder, you have to go to Settings>Mail,Contacts, Calendars.>Email account >Toggle OFF Notes. Yes, OFF. Sounds backwards. But it works. After you do all that and find your notes, toggle off notes for all your email in settings. Then toggle ON notes for iCloud. Do that and your notes won't vanish anymore. If you need further assistance, let me know and I'll do screenshots.