1. i'm wondering is it possible that fields which i pick up from fields list and place in column captions within list edit to be visible on userlist search only, but not all of them visible in user listing? e.g. there are 5 fields to be displayed in user search criteria area, say - name, age, profession, education, country; but in returned results , i.e. user listing, i want only 'name' field to be displayed. Is that doable?
Yes this is possible. Edit your userlist within CB > List Management then scroll to the bottom and have it disable all searchable fields instead of just searchable fields that are displayed.
2. is it possible to change wording on the buttons: 'Find' instead of 'Find Users', and 'Search' instead of 'Search Users'? which file to edit?
Yes, as they're language strings which you can find in your CB language files found below.
/components/com_comprofiler/plugin/language/default_language/default_language.php
Specifically the language strings "_UE_SEARCH_USERS" and "_UE_FIND_USERS".