Hopefully you have demonstrated to your satisfaction that you can make simple changes like color or font, and have confidence in the wordpress.com CSS Editor mechanism, right?
Assuming that it's just the Links and blogroll area that's at issue here: In general, CSS is not used for inserting or "editing" the html per se, just styling (and positioning etc) the html defined in the html or php file(s). CSS can insert html using :before and :after pseudo classes, but these are not well supported by all browsers, hence not a reliable feature (yet)
So CSS is a bit of a red herring when looking to get control of the links widget, and indeed that's not where the action is.
Most widgets have a title that is set within that widget's control panel itself (see other widget control panels). In the case of the Links widget, however, there's no such setting. That's because the links feature is intended to use the links categories as titles for one or more sections (of the sidebar), under which the links belonging to each category are listed.
So, with some links in the "Blogroll" category you'll see a sidebar section with title "Blogroll", with the links listed below. If there are some other links categorized as "XYZ category", that'll cause a sidebar section titled "XYZ category", and so on.
It appears that in the Blix theme you've chosen, that's not being done. Instead that theme generates a single section titled "Links", and list all the links in the one section, ignoring category.
So, I think you're out of luck finding an easy way to do this. It may be possible to do something sneaky, like adding a text widget for the sole purpose of adding some text that with clever positioning appears in front of the "Links"... but before going to those lengths it would be worth determining that you really do want to give up link categorization.
Hope that helps!