For example:
They often write in scripts:
By Sozdatel, etc.
And we know who made the map...

There definitely shouldn't be any of that.

A closed test is a test by a group of people (or even just one). At the moment, no one else has the right to receive the map, except for these testers.

Yes, but who will be in this group? Will the map authors be included? What level of gaming experience will the testers have? These are important questions.

Not quite correct: everyone who wants to can play, but already on a tested version, where there will be and should be fewer bugs.

In my personal opinion, there shouldn't be any bugs to begin with (with the exception of "bugs" in the balance of the Multiplayer game).
I think it's simply unacceptable to release a map with obvious bugs in the landscape, landscape textures, non-working scripts, etc., although I see this happening all the time :D
For example, on the Nival forum (formerly), I rarely saw maps without such "bugs."