Hello,

the theme change problem is probably a cache issue.
Make sure your module has, in the 'advanced' tab, the 'reset header' option set to 'yes' (when 'site mode' is set to 'advanced'), or just 'site mode' set to 'test'. You can also delete the cache folder mod_trombinoscopecontacts from the Joomla console 'System' -> 'Clear cache'.

As far as the menu item is concerned, the search field can be removed by setting, in the 'page display' tab, the 'search' to 'hide'.

Sorry, I misunderstood you for the menu item. I did not realize you were talking about the 'user contacts' menu item.
There is no option to remove the search field at this time (I will add it to a future release). 
In the meantime, just use CSS or create a template override of the view. It is better if you use CSS (so you don't have to worry about updating the override later on):

I have actually included the show/hide of the search and print options in the view into the next update, coming before next week