I think you have a fundamental misunderstanding about the Qt Project. It is not owned by Digia, Nokia, Trolltech or any other single entity. Respectively, there is no such a thing as a single entity approving something.
The Qt Project is developed by several different companies and communities. Digia is one of the key players. There is some chart somewhere how many commits are contributed by each participants. It is worth checking out. I think it is done by Thiago.
Now, let us reply to your questions:
Are they all developed with different open source communities voluntarily?
Yes, as you can see some is developed by ex-nokians, some is developed by the KDE community, and so on. So yes, they are developed by different communities.
Are these bindings approved by Digia to work properly?
No. They are mentioned on the community wiki page. Anyone can edit it, and add information to different bindings. These are just the common bindings, but no one guarantees "they work properly". For instance Qt Jambi does not work "properly" on Android, or PySide had no Qt 5 bindings when I last checked, etc.
That does not mean, however, they are not useful.