The second part--who did?--is a doozy. For years I've been intrigued by the Oxford hypothesis, but bothered by the contortions required to believe it.
In Sweet Swan of Avon: Did a Woman Write Shakespeare?, Robin P. Williams makes the case for Mary Sidney, sister of Philip Sidney. And what a case it is! Williams's research is thorough, her argument convincing. The chapter on Sources includes a 16-page table documenting striking connections between Sidney and many works known to have been sources for the plays. Williams includes a beautiful chronology, and the events fit Sidney's life in a way they don't for the other candidates.
Williams speculates, but doesn't require suspension of disbelief. Her argument works, and feels right in a way that others don't. Williams will be speaking at the Library on Thursday, and I'm eager to see her presentation.