Is there an API or a descriptive standard somewhere?
There's lots more. Just have a look at the Documentation page in the Developer References section.
The above links doesn't work. You can't get access the detailed api information. Is it possible to access the legacy information anywhere?
the first and third link do work for me though
Yes, your are correct. However, you get a "page not found" if you try to access Virtural Server (Command categories) under the first link.
It's coming soon. Those docs are auto-generated, and I haven't completed the port to make it work with the new CMS yet. I'm hoping to wrap it up on the plane today.
In the meantime, the docs are all available within the product itself (in fact, that's where they are generated from).
virtualmin create-domain --help
And the remote commands can be called similarly (all option names are the same):
And so on.