re: I don’t manage to mage the pagination work:
The pagination option are only available to the templates sold here if that template supports pagination.
re: Is it possible to edit the list of entries (to display only certain fields)?
If you do not enter info in the field, it is not shown. That said some templates will not display info even if info is entered. Most of the template sold here allow you to turn on/off fields via shortcode options if there is info entered for the field.
re: In case I would like to have a directory per city and speciality (a bit like yellow pages, is there an easy way to proceed ?
Use a template which support filtering by category and enter your entries assigned to the categories.
re: Is it possible to have a subscription-based inclusion in the directory?
No, other users use membership plugins to manage memberships and whether or not they have access to the directory.
Hope that helps!