Hmm, I had more or less discovered this on Friday (when uploading calibre-git to the AUR) -- but I was in a slight hurry and didn't realize creating ${pkgdir}/usr/share/desktop-directories in addition to ${pkgdir}/usr/share/applications allowed xdg-desktop-menu to work correctly.
Small note -- ${pkgdir}/usr/share/menus need not exist. Neither does ${pkgdir}/usr/lib/python2.7/site-packages, since https://github.com/kovidgoyal/calibre/commit/c4f232b967eb0ad8b9ab0b230149ed8eb6dc613f


While I am on the subject of tweaking calibre's PKGBUILD, python2-pycountry has not been required as a makedepends since a little over 4 years ago: https://github.com/kovidgoyal/calibre/commit/a30460bda8de79e1e71e2874ce4225c1eb6632e1
Additionally, resources and translations need not be built at all (and don't need to be commented out) unless you are building from a git tag -- the release tarballs already contain the built resources and translations.
And `python2 setup.py install` runs build, gui, and install, which means `python2 setup.py gui` should be added at the end of the build function, rather than being auto-called during the package function.
calibre no longer has any files which need to be patched to refer to python2 specifically.
Rather than patch the environment module location, you can set the staging-root to ${pkgdir}/usr instead of ${pkgdir} and the staging-{bindir,libdir,sharedir} will properly inherit their location.

Attaching new patch.

Oh, and come to think of it, xdg-utils should probably be a makedepends...

Thanks for the detailed input! Everything should be fixed.