YouTube live - unlisted vs private vs public videos

Question

When going live on YouTube live, you have an option to mark the video as "Public", "Unlisted" or "Private".
When you want to integrate your live stream channel into another website or application, you can easily link to the generic channel page, but only Public video streams are available on that page. (https://www.youtube.com/embed/live_stream?channel=[CHANNELID])
The video ID of every public video stream is also visible on that page when the channel is live.

Is there a way to detect if a channel is live using an unlisted video link and second, to find the ID of that unlisted video link without logging in with the owner Gmail account of that channel?

Answer 1

Is there a way to detect if a channel is live using an unlisted video link and second, to find the ID of that unlisted video link without logging in with the owner gmail account of that channel?

No there isn't.
Here are the main differences between Public, Unlisted and Private videos on YouTube.

+-----------------------------------------------------+---------+----------+--------+
|                       Feature                       | Private | Unlisted | Public |
+-----------------------------------------------------+---------+----------+--------+
| Can share URL                                       | No      | Yes      | Yes    |
| Can be added to a channel section                   | No      | Yes      | Yes    |
| Shows up in search, related videos, recommendations | No      | No       | Yes    |
| Posted on your channel                              | No      | No       | Yes    |
| Shows in Subscriber feed                            | No      | No       | Yes    |
| Can be commented on                                 | No      | Yes      | Yes    |
+-----------------------------------------------------+---------+----------+--------+

Please have a look at the official help site for more info.

Note: After all, if there was a way, then what would be the purpose of having them unlisted or private?