I have had the occasional bad download of a book. The usual fix is to force a download. I do this by deleting it on the device and then going to the site. In the "My Library", the book will be in the trash. Restoring it from the trash should put it in the "I'm Reading" list. The next sync should download it correctly.
The problem with the reading status not changing sounds like a corrupt database. This was probably caused by the crash. The database on the device stores all the details of the books including the reading status. If it is damaged in some way, you will see strange things like that. Fixing this usually means logging out of the device and restarting. This replaces the damaged database with a new one and takes you through the setup again. It will then need to download the books from Kobo again.
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