"Personally, do you consider your avatar an extension of yourself, or a character you control?...First, I mean your avatar, not avatars in general; I’m asking about the personal association between your First Life self and your Second Life avatar. Second, I don’t mean to present this as an either-or scenario..."
Both. Storm's a facet, an aspect; you can know someone for decades and there'll still be truths about them that you've never seen or imagined.
Storm's a creature of fluid appearance and gender, keeps an active blog, owns and runs a business, has friends and acquaintances, an email address...
Storm lives publicly while I'm a private person. When you look on Google for Storm Thunders, you'll find what you're looking for on the first page, many weeks the first listing; I'm close to invisible. Storm's an inventor and enterpreneur; I've never run a business. Storm is blunter than I tend to be, quicker to compliment or criticize, more willing to share opinions publicly. It has surprised me to discover that Storm's a bit of an educator, teaching inpromptu sandbox classes, offering freebies laced with learning opportunities, and answering questions on scripting groups.
I like to keep my "lives" fairly separate; it allows me to explore each of them without concern for how they rub up against one another. People respond differently to someone when they think they're of a particular gender, age, nationality, etc... I enjoy being able to explore those reactions and expectations.
Watching Storm's life and interactions has highlighted habits and reactions of mine that I was unaware of. People have far more power to affect their lives and situations than most of us ever acknowledge. I've learned a lot about how my choices of boundaries, socializing patterns and risk-assessment behaviors affect my life.
I find I'm more willing to get my hands dirty with unfamiliar technologies, more willing to tinker. I've become more confident interacting with strangers and discovered I enjoy teaching. I've grown less averse to some kinds of risk. I've been exposed to new music and artists, learned a lot about things like quaternions, using 2D and 3D graphical tools, and even learned a little basic marketing.