What I'd do is:
* Make sure the battery is well charged
* Do a factory reset via wi-fi, to rule out corruption from a bad cable or USB port.
* Don't restore the backup database, and don't sync with the Kobo Desktop.
* Transfer a few books via wi-fi, e.g. via sync if you have some Kobo books, or via the Calibre Content server for sideloaded books.
If the problems persist with just those few books then I'd really suspect a hardware problem with the device itself.
But if the problems have gone, then I'd try transfering the books via cable, only in small batches of say 100 books at a time, and check after each batch that all the books have been processed and are showing up in the library without problems before starting on the next batch.
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