If you want to make sure the second stylesheet loads after the first, you can use the third argument of wp_enqueue_style to set a dependency, eg:
wp_enqueue_style( 'styles', THEMEROOT . '/css/style.css', array() );
wp_enqueue_style( 'responsive', THEMEROOT . '/css/responsive.css', array('styles') );
As for having all the styles in responsive.css override style.css, that is going to entirely depend on the specificity of the targeting in each stylesheet, CSS being a Cascading Style Sheet, it would be worth researching exactly what that means if you aren’t fully sure how it works.
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