I think you have a fundamental misunderstanding regarding the Qt project. It does not belong to Digia, Nokia, Trolltech or any other separate object. Accordingly, there is no such thing as a single whole affirming something.
The Qt project has been developed by several different companies and communities. Digia is one of the key players. There is some diagram somewhere, how many commits are made by each member. Worth checking out. I think this is done by Thiago.
Now let's answer your questions:
Are they all developed using a variety of open source communities voluntarily?
Yes, as you can see, some of them are developed by ex-nokians, some of them are developed by the KDE community, etc. So yes, they are developed by different communities.
Are these bindings properly approved by Digia?
Not. They are mentioned on the community wiki page. Anyone can edit it and add information to different bindings. These are just general bindings, but no one guarantees "they work correctly." For example, Qt Jambi does not work “correctly” on Android, or PySide did not have Qt 5 bindings when I last checked, etc.
This does not mean that they are not useful.
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