I want to add as part of the definitive answer another application: b1 free archiver. More on B1 in the second part of this.
But first I want to mention some supplementary problems with the most used archivers .
What I am saying here may be limited to my use of Xfce/Thunar, so the conclusions may not apply in Nautilus and Unity.
Xarchiver and Squeeze do not seem able to open archives protected by password. Xarchiver gives an error and Squeeze seems to extract endlessly with no result (also, it cannot handle 7z archives, as far as I can tell). Archive manager can handle password protected archives.
Associating an archive with another archiver other than these three, like Peazip or B1 and using a context menu command like 'extract here' would open a window prompting to select as archive manager one of the three mentioned above.
I am not aware of a solution to this problem in Thunar (which is also mentioned here in relation to PCManFM). But b1 has options for Nautilus to integrate the context menu - see the end of this answer.
Now, concerning b1 archiver.
In a way it may partially be a solution to the Thunar's context menu problem as it does not really need the context menu association: unlike Peazip, with B1, associating an archive type and opening it (e.g. by double click) would open a window providing a list of options, each of which can be set as default by checking 'remember my choice' or by setting the default action ('ask me' is the action by default). That is, if so decided, the archive can be extracted just by double clicking on it.
B1 is able to handle (open and extract) the most used archive formats as well as its own type.
But it is rather limited when it comes to creating archives: only its native format and zip (with no advanced options) are supported. Even worse, I was not able to create a b1-archive: the process ended invariably with an error. Zip-archiving works. I trust this will be fixed soon.
(Oddly, the program settings do not seem available from the main interface (when just executing the program), but only from the smaller window - clicking 'Set the default action'.)
This archiver provides the main info demanded in this question, and also looks more elegant than other solutions.
It seems that the program can integrate the context menu in Nautilus.
There is a a new (beta) file manager that provides, among other features, the required info during archive extraction: Polo. It comes from the creator of other popular software (Grub Customizer is one) - more here: TeeJeeTech.
sudo apt-add-repository -y ppa:teejee2008/ppa
sudo apt-get update
sudo apt-get install polo-file-manager
It shows something like this during extraction (click to enlarge):
(details depending on the theme; in the above image it follows the gtk3 theme Victory-16.04 in Xfce)