responsive-1 is the layout file for Xi. responsive-2 isn’t used (future use!).
Copying css files into your child does not do the same thing as copying template files like header.php or single.php etc. WordPress spots the alternative template files but it cannot do that with the css files.
If you look at the example in the child theme docs at the bottom of page about creating a fully custom stylesheet. In this example I do the same imports that the parent does but then pull in my own layout.css (in mu child theme folder).
But I must then reproduce the rest of the styles that were in the parent style.css in my child css.
Changing responsive-1 can be done this way. But just a few edits can be done just by overriding styles in the child’s style.css.
In terms of the drop down menu, it is not really all that responsive. It is a pure superfish menu but it does actually dynamically adjust to the longest item. It uses the supersubs script. The min and max width of these are set in javascript to be 12em and 27em. See js/tricks.js.