Users accounts – Contributer and Place owner

Listing owners can reply to any comments, just like anybody else.
Their username will be shown, so it should be clear that it is the owner.

Listing owners also can insert promos, add/change details etc, from their dashboard.

Basically, all your users get a subscriber WP account; listing owners can edit their own listings at any time, and anybody can comment if that is how you set it up.

Does that answer your question?

From GD’s point of view, it is all set up automatically.
A listing owner is the person that submitted the listing; that person will be able to edit the listing (and admin of course).

At WP > Settings > Discussion, you can choose whether anybody can comment or people need to be registered before they can comment.

If you do not want to use any other plugin, follow these steps to force people to verify their email address:
1. WP > Settings > General > Membership > Anyone can register > YES
2. Implement http://docs.wpgeodirectory.com/redirecting-the-login-page/
Redirect to wp-login.php
3. GD > General > General > Allow user to see wp-admin area > YES

If you want to approve new users manually, there might be a plugin for that or you can create your own form.
It might be simpler to review listings before publishing:
GD > Design > Listings > New listing default status > Draft

I hope I am making sense.

If you mean that you manually want to authenticate each user, yes. That is not part of any normal WordPress and therefore not GD.
If you mean that the user authenticates themselves by using the password sent to them by WordPress, then you do not need anything else, but follow the steps I set out.

Maybe we misunderstand each other, when you say user authentication.
Normally admins do not approve each and every new user, but users need to verify their email address. The last option is standard GD and WP as explained.

Can you describe what you mean with user authentication?

If you want users to have additional permissions, then you might need something like https://wordpress.org/plugins/user-role-editor/

If you want some users not to be able to access certain pages, then you might need something like https://wordpress.org/plugins/s2member/

Without knowing exactly what extra permissions, enhancements or access you mean, it is difficult to be specific.

OK Amir
What you described in the last post is exactly what GD will do for you without anything extra to be implemented.

Shop owners can submit a listing, and can add all these things.
And customers can communicate if the shop-keeper adds an email address to their listing. That will add a contact form to the shop’s listing page (you can see that on your london listing page).

There is really nothing additional you need to do as per your description.

Try adding a listing as a shop-owner, you already have the Add Listing added to your menu. Just logout as admin, or use another browser. That will show you how it works. Or have a go at the demo at http://wpgeo.directory/

You will need to enable user registration, before you can add a listing as another user.

That is all you have to do to implement what you want; it is all set up already.

I also suggested this if you did not want to use a 3rd party plugin:

If you do not want to use any other plugin, follow these steps to force people to verify their email address:
1. WP > Settings > General > Membership > Anyone can register > YES
2. Implement http://docs.wpgeodirectory.com/redirecting-the-login-page/
Redirect to wp-login.php
3. GD > General > General > Allow user to see wp-admin area > YES