When and how did Bitcoin start? Exactly when was the first block mined and the first bitcoins generated? How many people knew about the project at this point? Had the project been publicly announced before the first block was mined or did that happen afterwards? Is there anything special about this first block or could anyone have mined it?

I realize that there are a number of questions included here but I don't think that it makes sense to ask them separately.
Bitcoin's design paper was published on cryptography@metzdowd.com on October 31, 2008, which is considered by most to be the official beginning of the project. On January 3, 2009 at 18:15:05 GMT the Genesis block was established. Six days later, Bitcoin 0.1 was released and announced on the Cryptography Mailing List.

It is hard to estimate the size of the community at any point, especially historically, but there is a decent timeline of the major events in Bitcoin history at the official wiki.