To address the first question: Yes. You do have to. A blog is the easiest way to brand yourself. You control the content, you control the impression and personality that you're sending out. It's really important to create an online persona--a brand--that's separate from your personal life. Recognizing a distinct line between who you are online and who you are in person is vital to avoiding the "oversharing" faux pas that plague social media users. We'll talk more about that, too.
Your blog serves as your hub. You can direct people from your Twitter, Facebook, etc. back to your blog for contact information, info on how to buy your products (even unpublished, you're selling something--don't be fooled), and a cohesive view of who you are. Things get really fragmented out on the Twittersphere.
Of course, the major drawback is that the blog doesn't post stuff on its own (Conspiracy??? I think so.), which means you have to develop a posting schedule and stick to it. Three times a week is pretty ideal. Less than that and things just look sparse.
How to get started: claim YourName.com and create some blogs (yourname.blogspot.com, for instance). Then write up a few posts--maybe two weeks worth--and schedule them to post automatically when you're ready. That'll give you some cushion as you get into the rhythm. Of course, if brilliance strikes, you can insert the post in place of a scheduled one. Then you'll just have a post saved up for a rainy, uninspired day.
Tomorrow: Blog Content. Avoid word vomit. And ruining your career.