List Categories (as posts) list of posts inside

Hello everyone.
What I need to di is:
1) Somehow list categories (excluding by ID those I don’t want to be listed) whether on the page or using another php template file
2) Categories should be listed the same way as posts (look exactly like posts)
3) Inside “post” body (Let’s say Category name is a title, so after title there is post body. As I said “exactly like posts”) list all the posts from the category – just links