Backport improvements from Python Project Template.
Pass entity manager through update methods.
Re-arrange order of API documentation.
Remove useless :undoc-members:.
Bump Sphinx version.

This is to account for this bug, which claims to be fixed in 1.2, but is
still manifested.

https://bitbucket.org/birkenfeld/sphinx/issue/1337/autoclass_content-both-uses-object__init__
Tweak README wording.
Update API a bit and improve API docs.
Test different instances of same component type.