You ask several related questions, but this is the main one, I think:
How does one find out what name emacs gives to a key such as the one labeled pause/break on my keyboard?
For Emacs's description of a key, use C-h k.
So C-h k, then hit the Pause key. Emacs probably tells you this:
<pause> is undefined
So you now know that Emacs describes that key ...
Yes! This is command-log-mode which can be installed from Melpa.
You have to add the function to whatever modes you want to record, like
(add-hook 'python-mode-hook 'command-log-mode)
Then, to invoke the log window as shown in the video
Open a Python file (in my example) and start manipulating the code to see your ...
If you don't have a Meta key (it is often Alt) then you can use Escape, yes.
But in that case, what you want to use is Escape followed by Control + f, which we write as ESC C-f.
That is, Emacs writes the key sequence as ESC C-f when it talks to you about it.
A Meta key, which we write as M-, is a modifier key, which means you press and hold it down while you ...
Don't try to create one .emacs file for all your environments and conditions under which you might access them unless you have time on your hands.
Longer answer for those who might be in a similar circumstance...
How to troubleshoot
Thanks to the input from commenters and others. I'm putting things that helped be get to some of the issues.
Is there any package that does that, or a way to achieve it?
One such package is Show Key (code: showkey.el).
Global minor mode showkey-log-mode keeps a log of such events, in a separate frame. It's refreshed with each new event, and it's kept on top of other frames without stealing the input focus. Various user options control what events get logged, etc.