How do I redownload kindle books from Icloud?

Hi, I just did an accidental system upgrade on my Ipad (got a message, thought they meant "update", so I clicked it and the upgrade started 😝). Anyway, works fine, except now I can't access any of my Kindle books. When I opened the Kindle app, it asked me to use my e-mail and password to register. I did, but now when I click on any book, I get an error message, saying I need to redownload it from Icloud. How do I do that? I also said I could deregister and register again, but then there was a warning that all my books would be erased then.

I also noticed that the name of my device for Kindle seems to have been automatically changed to "2nd Ipad", when before it was just "Ipad". How will that affect future downloads (on Amazon there is still only the old name, so if I buy a book there, will there be an error, too?) I haven't really used Icloud yet, except for the automatic back-ups it does when the device is plugged in. So, how can I save my Kindle books, as well as future purchases?