How to modify wp-includes without messing my wordpress installation?

You won’t want to modify any files outside of wp-content unless you’re alright with them being blown away during an upgrade.

The best way to modify what you’re talking about is in the styles.css file located in the wp-content/themes/twentytwelve folder. This way you just override the specific styles you’re not happy with and don’t need to worry about upgrades breaking your code. If you want to get a little more advanced, you can start modifying the functions.php and header.php files which house most of the functionality you’d need to modify.

The nav-menu-template.php file you’re referring to in wp-includes is just a file that processes in the background and outputs data, the actual visual display is probably in header.php and pulls it’s design from styles.css.