Headers and Widgets

Hello, First of all, here is my website : http://constitutiontime.com/ I have some problems and I would like some help (I'm french so I will try to explain myself the best I can). 1. On the homepage of my website, you can see a header (an office with a globe etc.). Then, you have the categories (France, Russia, China etc.). I created a special header for each of these countries. I will take the example of France. When you click on "France", the image that I created appears, it is different than the one that is on the homepage. But, to obtain this result, I had to create a page, not a category, in order to put it directly in my menu. That is a problem. Because I cannot ad an article to this page, it should be a category. Look, I wrote articles about law in the US. I would like to put it in the category "united states". What you see in the menu is actually a page, not because I wanted it to be like that, but because it was the only way for my special header to appear. If I want my headers to be different than the one on the homepage, I have to put it as a page feature. Only then, It will appears. Is there a way in which the header can be different for each categories without requiring a page ? 2. About the widgets. The widgets on the homepage are the same than on the other categories. Is there a way to change it ? I would like some photos on the homepage (gallery) and others in the other categories. Sorry if i'm not clear.