This happens because your frontpage/homepage menu item ID stays the same. In other words, your image & intro modules continue to show because they are assigned to your frontpage menu item and that menu item's ID is not changing when you navigate to a K2 item.

In Joomla we use menu item IDs to differentiate content loaded. In your case, the menu is pointing to a K2 category so when you click on an item, the menu item ID remains the same and K2 displays the item. To bypass that, do the following:

- Make your homepage menu item point e.g. to Joomla's Featured Articles. Make sure you don't have any marked as featured so the output will be empty.
- Below the intro text, add one more module of "K2 Content" type. Use that module as you did with the K2 category before: retrieve K2 items from one or more categories. Make sure this module instance, as well as the homepage image and introtext are shown ONLY on your homepage (from the module menu assignments tab of each module instance).
- Create a new menu item pointing to the K2 category (or categories) with your actual content. This content is what is also retrieved in the "K2 Content" module I mentioned previously. Now, this new menu pointing to K2 categories should appear in your site's menu. If you don't want that, create a new menu in the Joomla backend and just don't call the menu through some menu module.

Now when you click on one of the K2 items in your frontpage, the menu itemID will change and as such, any module that was previously assigned to your frontpage menu item will now NOT show up in your K2 content BECAUSE it has a different menu item ID and BECAUSE the modules are not assigned to that menu item.

Got it?

P.S. This is Joomla stuff really, it's not specifically related to K2. The same thing would happen with Joomla articles as well, only (worse) Joomla articles have their options set in the menu item and not their category, so you can end up with the same article page but different assigned modules or article page options based on HOW you ended up to the given article. This whole menu item IDs thing may seem a mess, but it's actually very powerful if used properly.

Replying...

1. An article overview does not contain other items, just the item you see. If you mean categories, then how items are presented in what you see is controlled first by the respective K2 category or if you're creating a menu item pointing to multiple categories, some parameters like the grid are controlled by the menu item options.

2. Not out of the box. A plugin is currently being tested for that and will be released in September as part of the K2 Pro suite of extensions. See a preview here: www.nationalopera.gr/en/alternative-stage/es-children-s-performances/item/2250-the-emperor-s-nightingale (language switcher is on the left sidebar).

3. When K2 content is assigned to a menu item, the URLs are indeed simplified. But I did not suggest this change for that. You need different menu items if you need your layout (=modules) to be different across pages/sections.

Again, if you don't see K2 images in some view, they are either hidden in settings (K2 categories, K2 modules etc.), or if you use a 3rd party template, they may not have been included in the template overrides.

As for your CSS example, it would really only make sense if you provided your site's URL, so there is context :)