For starters you should only be copying the .epub file to your reading device. The .opf and cover.jpg files that calibre stores for each book are only meaningful to calibre. The .opf file contains a backup of calibre's metadata for the book. The metadata and cover used by most android reading apps is that which is stored inside the .epub.
If you use calibre's Save-to-disk option (rather than drag/drop or copy/paste) you would have the options to
- exclude saving .opf and cover.jpg
- use whatever folder/filenaming structure you like by setting the Save template
- calibre can update all its up-to-date metadata into the epub during the save
See calibre
Prefs - Saving books to disk for more details.
Alternatively, if you haven't already, you might like to check out the android
Calibre Companion app which is a very nice way of managing your books on android devices. You should still be able to use fbreader for the actual reading of each book, but I haven't tried it as I prefer Mantano, Moon+ or CoolReader myself.