You can edit in HTML-Kit regardless of what browsers and devices you're targeting but HTML-Kit Tools in particular also makes it easy to preview on those devices while you edit.
I'm assuming you've already picked a mobile-friendly/responsive CSS framework. There are dozens of them like Bootstrap and Foundation.
Edit HTML as usual. Use CSS classes provided by the CSS framework of your choice so that page elements know how to flow with the screen resolution.
And then test for various resolutions in the Preview window:
At some point you'll want to test your pages on a real phone or a tablet. So it's possible to edit in HTML-Kit Tools, use the built-in Preview window, and, at the same time, preview on external devices:
Hope this helps!