If they are .mobi books obtained from somewhere other than Amazon, it won't make a difference what account the device is registered to, or if it is registered at all. Airplane mode is irrelevent.
Check if there are any odd characters in the filenames of the ebooks that you put on the Kindle. I'd remove any character that isn't a letter or number from all filenames.
A restart done via the menu might help. A factory reset would be the next step if a regular restart doesn't work.
If that all fails, the next thing I would do is import the books into
Calibre, convert them to .mobi (even though they are already in that format), and transfer them to the Kindle using
Calibre.