Please report any bugs you find on the GitHub bug tracker.
Yes, you can download gh-pages.zip (~30 MB), extract it and open the index.html file with Firefox or Chrome.
In case of Chrome/Chromium --allow-file-access-from-files has to be passed on start to enable all features also available in the online version.
This API reference includes all libraries included in Debian testing/unstable. If the library you need is missing it might not be in Debian yet or is no longer included because it no longer has any users in Debian.
I use Debian as a source because it tracks upstream GNOME reasonably fast while still including libraries that are not part of GNOME.