I would like to have a second menu ( if possible a "drop down menu )
on a page that doesn’t have the menu items like the rest of the website, and also pages that are marked as “don’t show in menu bar”
You can place menu items on any page. If it’s a menu that isn’t going to be part of your main site navigation, be sure to not select the add pages automatically option. This way, you have full control over how the menu behaves and what the options link to. Menus do not have to appear on every page, just make sure that your custom menus are not included in a group that does show on every page.