1. Does links from social media like FB, twitter matters? (how much does it matters compared to traditional links)
The short answer is "we treat all links the same", we look at PR of the backlinks and reputation. It doesn't matter where it comes from, .gov or .edu.
But links from FB might not pass any juice because it's a private page so Google can't fetch them and most links from twitter are no follow.
Source: Matt Cutts New Q&A Video