This page shows how to create the embed code for any Facebook video to embed them in external websites.
Is there a way to start the playback automatically on page lo
Unfortunately for you Facebook's policies forbid the autoplaying of content (thank god).
I have attempted to track down the actual policy document but it's been drowned out in the SERPS noise of people talking about it being banned on Facebook!! You can find questions that back this notion up on StackOverflow and WebApps.
StackOverflow is the official Facebook developer support channel so their users may know more on the topic.
It's also possible some whizzy jQuery might be able to fake the click, - but facebook updates it's code so often that I doubt any hack would last long.
Best answer is use YouTube or another channel that allows you so share outside their network. Don't rely on a hacky solution for a network that clearly isn't interested in video being shared beyond it's own borders.
Users can easily change the privacy settings on their videos, and Facebook will probably try and disrupt the ability to embed their content if it becomes a popular thing to do.