Set the menu link as disabled by default When I create a new node its menu link is enabled by default. I would like to enable it manually only in case if I need. 
Is there a way to set the checkbox in menu tree as uncheked by default?
Have a look at this module, I guess that is what you want.
http://drupal.org/project/default_menu_link
Some details from the module's project page:

Provides the user with a check box on all content types to set the &quot;provide a menu link&quot; value to true by default.
This is basically a nice way to ensure the menu system is adhered to by all content authors.
There is a similar module called menu_force that does just that. Whereas Menu Force mandates menu assignment, Default Menu Link merely changes the status of &quot;Provide a Menu Link&quot; to true. The user can still create content and choose to un-check this box. However, the default state (on node creation) will be true, and as long as you've set a default menu parent item, all content will be filed under that parent.