The answer to the original question (at least for older versions of IE) is that media queries in a SINGLE stylesheet do not work and so it is necessary to add the additional stylesheets as detailed in Chris’ article. See the ‘Browser Support’ section.
Following this issue you DO, in fact, have to redeclare all the rules again (as required for the individual resolutions) otherwise they would not apply.
In general, it’s best (IMO) to create a stylesheet for the lowest resolution you are going to support and then add rules to the extra stylesheets as the resolution requires.
In that way, you do not clutter your, for instance, mobile.css with rules that won’t ever apply.
You can always make an existing site responsive and that’s why, few points you should keep in mind.
1. The layout
2. Creation of media file
CSS3 has already the media file function and for that, this is quite appropriate for making an existing website design responsive.