Wow.... Did you check for gremlins?? That is just wild!
On the plus side, it's nice to get a funky new problem to think about rather then answering the same 3 questions over and over
In the first place, remove that epub you transferred from Calibre from the Kobo, and keep it off while debugging this issue. That file itself could be corrupt and causing this issue, but lets eliminate it from the equation for now. If we fix the problem, and it reoccurs right after you load that epub back, we'll have a fairly good guess at the culprit.
First log into your account at kobobooks.com and completely clear your I'm Reading list. Then sync the Kobo to clean out the books.
Then sign-out of your account on the desktop app. This SHOULD delete the local copy of your purchased books that might have gotten corrupt somewhere along the line. Then log back in, re-add the books to your reading list through the website, and update/sync the books back onto the Kobo.
No? Try fully uninstalling the desktop app, and reinstalling. I've really never heard of anyone having covers not showing up in the app, so lets just cover all the bases before we get more extravagant.
(NOTE: It really sounds like, somehow, your SQlite database got borked. So if all else fails, you should be able to completly wipe the database and start with a fresh one without problems. You will of course lose all the 100-free books this way, but I wanted to through it out there so you know there is a last ditch option)