There are two ways you can go about adding a view to a menu (in both cases, this code should go into the template of the specific element in question, eg. the template for the menu, etc) you could have the menu render the view, or have the view render the menu, I’ll give an example of both, though I expect in your case having the menu render the view might work better, since you’ve already got the menu.
Menu renders view:
print views_embed_view('machine_name_of_view','machine_name_of_display');
(If your view has contextual filters, you append them as additional arguments (this probably won’t apply to you):
print views_embed_view('machine_name_of_view','machine_name_of_display',$node->nid);
View renders menu:
print drupal_render(menu_tree('machine_name_of_menu'));
You can grant access to the view itself through the view UI (edit the view and look in the 2nd column). If you are exporting blocks and/or pages, they have their own set of security that you will need to grant permissions on (for example, configure a block and click the Roles tab.)
Stock Drupal ships with the concept of Main links and Secondary links. You get to choose which menus are actually assigned to those two classes of links. That is done in the Menu Settings (/admin/structure/menu/settings) page. The default mapping is: