I think the default setting for Facebook is to load the mobile version. If you scroll to the bottom of the Facebook mobile site, there's a link to switch to the full site. Or, you can try this:
Type "about:debug" in the browser, and then you can see a lot more options in the internet options, one of which is "UAString". Click this and choose "Desktop".
Also, have you tried downloading Flash 10.3 in the Market?