It depends on where you tell Calibre to send the books. Your Library is where ALL of your content is, and then it's broken down by format/location. So you have separate sub-libraries for Books, Files, Apps, Movies/TV etc. Anemic Oak has a photo of it
here.
If you tell Calibre to send your books to the Books folder on the internal memory, it shows up in the main Books library. If you send it anywhere else it seems to end up in the My Files library/file browser. On the other hand, it seems to be smart enough to detect that videos are videos regardless of where they're sent, and those all show up in the Movies/TV library.
If you do a search from the search bar at the bottom, it will search all libraries at once.
I also send from Calibre with the series in front of the title. I don't know how it deals with that when you send stuff to the Books folder, as I haven't done that yet, but I expect it to work fine since the Color did. It doesn't seem to show up when you
browse the Files directory, but it does when you
search your library via the search bar. That's good enough for me, as I usually use the search bar rather than browsing, but that may not be enough for others.
I don't use Dropbox, so I'm no help there.
Yes, sideloading apps seems to be possible, but I sure as hell couldn't make it work, so I can't give any information there either.