1. How to hide the search box on top right of the interface?
Use the show_search preference setting (i.e. show_search=0)
http://xataface.com/wiki/preferencesHow to hide some fields from the search form? (i tried visibility:find = hidden but it is not working; when i print_r the field in SearchForm.php it gives me $field['visibility']['find'] = visible)
visibility:find=hidden is the correct way to do it. Check to make sure that you don't have 2 sections in your fields.ini file for the same field. The 2nd one would override any options you set in the first one.
3. How to show calendar or select widget in search form for date fields? (in add form it displays right with widget:type = date, but not in the find form)
Currently this is not supported. Users have to enter dates manually for searches currently (unfortunately). You could implement this yourself by overriding the correct blocks and slots... but I don't have any code samples specifically showing how to do this. Perhaps in a future version this feature will be added.
-Steve