Definitely, It will carry social signals to your website. Social signals are one of the ranking factors in Search Engines. Also they drive traffic to your website.
Not necessarily. It may generate some traffic to your site, but Facebook pages alone can't rank your site in the first page. But its not bad to add it up to your link building methods.
I agree with the above post, it doesnt play a MAJOR factor, but it can build traffic for your site. What is important is using other social media sites like Digg, Mixx, and Reddit, that allow you to post content and information that is relevant to your niche/market. Those sites will grant you quality backlinks and also send more traffic through to your website. Facebook is good for networking and the FB Page is important, but do not spend too much time there.
Yes, if you are a celebrity with good reputation in your field and have many followers, your links are quality links.... Matt Cuts: "We do use Twitter and Facebook links in ranking as we always have in our web search rankings, but in addition we’re also trying to figure out a little bit about the reputation of an author or creator on Twitter or Facebook"