I've never used Calibre with a phone. I do have a Kindle, which has had WiFi turned on exactly once (to activate the device) and off ever since. I connect it to the computer, fire up Calibre, then tell it to send books to the device - that's it. I download books from different sources, but even when I get them from Amazon I see no reason why they should know when/how often/how far I've read, even less what other books I put on my device, and so I'll always download to a computer and sideload to the device.
With a phone I'd just copy to the phone's internal storage and tell an ebook reader to import them (though I don't really use a phone for books - I have some on there, but can go all year without opening the app).
So I guess you are talking about a Nook app. Which raises the nasty possibility that the app stores the books in their "private" storage (/data/data/<app package name>) where you can't see them except by using the app. That's the sort of control-freaky way these outfits work, but will be very difficult for you if the app no longer functions.
It certainly seems to be how "that other one" works: I just downloaded a book to the app on my phone (for the first time) and can confirm that it doesn't appear in the "kindle" folder on the internal storage, nor could I find any option to export it (these corporations want to control your access to the material you have "purchased", so this is no surprise. It's also part of why I refuse to play their game). If B&N take the same attitude then the solution would be to download another copy of the material you have purchased to a different device, except that if they are gone that won't be an option.
This is another reason why I don't buy into the "keep your media in our cloud" business model that so many push these days: if I pay for limited-time access ("rent") that's one thing, but if I buy something I'll have my own copy in a portable format that I can play on any device whenever and for as long as I want, and if that's not on offer they don't get my money. If the corporation retain control of how you can store and use the material that also means that when they can control when you can no longer use it, either directly (these corporations have withdran DRM-protected books after people had bought them, rendering them unreadable) or indirectly by discontinuing the service, leaving you unable to access your content (which sounds like your problem here).
I don't ever rely on cloud storage for the same reason. It may be convenient, and I use it on occasion, but I never rely on it: if you haven't also got your own copy under your control then exactly the same can happen whenever they decide that it's no longer in their interest to keep your stuff or to let you access it.