The solution is the solution exam for the first exam version.
The catalog should contain solutions of all questions in the group you picked questions from. Test it if you need to know what's be in it in your case!

I tried it, but I wanted to know if I understand it correctly, hence the question.

The current behavior I can see is:
- The solution shows only the solution for the first exam. (What about the other ones?)
- The catalog shows all the questions (regardless if they are in an instance of an exam or not).

So, if I want to give the answers of all the questions picked for the current exam, how can I do it? (if I don't want to disclose all the questions I used to chose from)
The solution button only shows the first one, if I created 10 different exams, how can I obtain the other 9 solutions?

This is not available.
One solution is to give each student his annotated completed answer sheet (PDF), so that he can see his errors.

I see. My institution needs to archive one copy of the solved tests (not marked by the students).

How the solution button works? can it be tweeked to create the other solutions?
Does it invokes some command?

The solution is produced by auto-multiple-choice prepare --mode s, which runs LaTeX on the subject with the correc package option.
Tagging used questions from your group is not implemented in tha package, so it won't be trivial to get only the questions that are used in the exam versions.