Sadly no, wordpress doesn't provide hosting (apart from the free one of course). You won't actually lose any data if you export from your current site.
If you aren't feeling so comfortable with transferring everything yourself, you can actually pay WordPress for a guided Transfer for $129, they'll install everything, transfer everything over (including followers), point your domain to the right place and even help you out for two weeks with any questions you have. More on that here: http://en.support.wordpress.com/guided-transfer/
You can find the 'recommended' hosting providers here: http://get.wp.com/hosting/
With google analytics we have stats here which do a pretty good job. And for adsense, you can sign up for wordads since you have your own domain: http://wordads.co/