On the home.php you can use a customized Loop (see http://codex.wordpress.org/The_Loop). Be aware that using home.php
it will display instead of your index.php.
For the news.php the same solution (though when clicking on the category link “news” it should display only posts from that category).
Regardless which solution you choose, it’s always good to start with the Codex: http://codex.wordpress.org/
There is a better way, actually. All categories can be displayed individually with little or no effort with the use of the category.php template. You can customize them very easily too.
See: http://codex.wordpress.org/Category_Templates
To see customized categories in action, visit my website at this category to start and click around the different categories to see it change. It is the example used at the bottom of the article in Category Templates using one category.php template file filled with variables to generate a unique category page for each category.