Assigning posts to a specific page

I want to assign specific posts to a specific page [template].
So for example, on my "video" page, I want to assign all posts under the "video" category to that template. For a different page [template], such as "Travel" I want to assign all the posts under that category to the "Travel" page [template].

I do NOT want to lump all posts in all categories under "blog".

Also, although I do have global regions, I want these to look different and not be global. For example, the "video" page has a certain header/bg, and the travel page has a different header/bg. I see when you save a new posts, there is a pop-up asking if you would like to assign the layout to posts of that type or just that post.

Here are the problems I am having:

1) I have content that already exists, and the theme doesn't seem to want to apply any layout to that content, even if I make a new layout and assign that post to the appropriate category.

2) Also, even when I correctly assign posts to a particular category, and when I click on the individual posts(like my "video" posts) they show the correct layout(the "video" layout, when I click the category it shows a blog layout and not my category layout, so I need to be able to get in and alter that as well. Perhaps this has something to do with the slug? Because the slug is blog/category/videos, so I would assume that something in the theme is telling it that it needs to show a blog layout. That's just my thought but I don't know how to fix or alter this. The main reason is that I plan on linking each category in my menu, but I can't do this if it's not assigning the correct layout.