I am a Silverstripe newbie, but know my way around HMTL & CSS and have recently studied Responsive Web Design.
I am wondering how I go about making an existing non-response/ mobile un-friendly website responsive?
I have access to the websites CMS, but not to the Templates yet (I am waiting on access) - Am I right in understanding that the HTML cannot be edited via the CMS?
HTML cannot be edited through the CMS. The idea with responsive is you use the same markup between desktop / mobile so to make a SilverStripe site responsible, the very least you need to do is add your responsive css as you would any normal website. Nothing is SilverStripe specific with responsive (unless you want 2x content images).