Display some content on selected pages My project runs on Drupal 6, and I'm using Views. 

I have a main menu with two submenus (menu -> sub1 -> sub2). 

This image shows what it looks like on my "edit panel."



The box with an orange border is the second submenu, and the one with a black border contains the item content assigned to this second submenu. 

All the items from all submenus assigned to first submenu (main menu -> sub1 -> sub2.1, sub2.2, sub2.3 ...) are showing up already in the first submenu. (Th first submenu is a drop-down in the main menu; I don't want to have all submenus in the main menu, but just the first one.) 

I want to hide them from there and display only the item that belongs to ie. sub2.1 or sub2.3. When I click sub1, I see all items from all sub2; when I click sub2.1, I see the correct items assigned to this submenu.
To understand what may be going wrong in your attempt it would help to clarify a few things about which modules do what.  


Your menus are handled by either core menu or another of the menu modules that build upon it.  They display links and and any selection reroutes the browser to a new URL.
Views is a User interface to query the database in which all of your content is held.  If you select the settings tab in the main views page you can set the actual SQL query to be displayed in the preview area.  This is helpful in understanding what is being searched for in your settings, although you will need some understanding of queries to make sense of it.  A view is called either by using the defined path in the URL or by placing the view in a panel (Which you have done here).
Panels is primarily a module to handle the display of content. However, it works very closely with Page Manager module.  
Page Manager intercepts URL requests and acts upon them in accordance with rules you establish for selection and contexts.  Panels and Page Manager collaborate together and switch between themselves regardless of where you start in the UI.


When you select a menu item it is requesting that the browser go to a specified URL (menu).  That URL request should be requesting the panel page (panels and page manager) which in turn is requesting the view that you have placed in it (Views). For your example, once the request  is made menus, panels and page manager are done.  Your real issue is with the views, so you must focus on the view module and your definition.

In order to help the view distinguish between various levels of content you can add a field to the content type that defines its level. You can then expose that field to views by selecting it as a filter and setting the value you want for that article.  You can create multiple view pages within the View definition to address different filter settings needed for placement in each of your panel regions. By categorizing the menu-selection/articles and providing separate view pages (within the same View definition) you can refine your control of the displayed content.

You can also limit the number of articles displayed by a view by selecting the options under pager in the view definition page and telling how many pages/articles to display.

You can learn more about Views at nodeone.se