As for hte problem you are having with the mystyles it should make use of the same file regardless of weather or not you are working on the index page or any of the other pages that are derived from a template. If you look at the reference in the index page it should appear the same as the references on the pages derived by the template. The location of this file should be:
I might not have explained precisely what I want. I have a situation, where styles that have the same name in home page and contents page need to get different layout. For example I want to dimension the HEADER differently in Home page and contents page. To do that I need 2 style sheets. One for home page and one for content pages.