Applescript to read facebook notifications
AppleScript is built by Apple, for Apple (though unfortunately support has steadily declined since the move from 10.6.8 to 10.7)

While it is possible to do what you describe with AppleScript (or any language, with enough blood, sweat, tears, and coffee), it will be much more difficult than using Facebook's API to view your notifications (or using OS X's built-in Facebook plugin). 

As far as scripting Chrome with AppleScript, Safari will be easier as it has some built-in hooks. I'd start with something to download a YouTube video (non-copyrighted, of course) using Safari, else you may get bogged down in authentication and trying to parse HTML, rather than actually having fun coding.