replace old theme with responsive

You don’t replace theme, you just switch theme.

Before that, you would have to customize the design of Responsive Theme to match your current site, the design will not and can not be 100% same exact because the HTML structure is different, but mostly you could make theme look pretty close.

In WP, you don’t directly edit the theme file, instead make a child theme to hold the customizations.
http://codex.ww.wp.xz.cn/Child_Themes