Danny Sullivan has published an excellent article at SearchEngineLand about Social Media signals and Google search results - and Bing as well. He's not just making general observations, either. He actually interviewed spokespeople from these two predominant search engines.
1) If an article is retweeted or referenced much in Twitter, do you count that as a signal outside of finding any non-nofollowed links that may naturally result from it?
Google: Yes, we do use it as a signal. It is used as a signal in our organic and news rankings...
3) Do you calculate whether a link should carry more weight depending on the person who tweets it?
Google: Yes we do use this as a signal, especially in the "Top links" section [of Google Realtime Search]. Author authority is independent of PageRank, but it is currently only used in limited situations in ordinary web search.