I think you're probably referring to the Calibre content server.
The Apple subforum is better suited for your post. More likely to get more advice there. Perhaps you can request the mods to move it there.
Calibre Companion is an app for iOS and Android designed to help you transfer ebooks from Calibre to your mobile device. I recommend giving it a try.
That said, if you only have a 1st gen Mini (max iOS version 9.3.5), why not install an older version of iTunes that still has iBooks support?
http://www.oldversion.com/windows/itunes/