An entire section devoted to your popular answers from Stack Overflow would be very very much welcome.
So yes, we should definitely create a new section for them.
I only worry about the name- a menu bar link to FAQ might be interpreted as frequently asked questions page about the doc-site, rather than a section devoted to frequently asked questions about the language itself. (Of course, it could just be me who perceives FAQ in this way, I'm open to others' opinions)
An alternative could be that we include them on the front page (maybe summary versions of like 5 of your Q/As, randomly chosen per pageload), and then a section called either "Scala FAQs" or "Popular Questions"?