Yeah, I run all my RSS feeds from my Web sites through FeedBurner service and love it.  I don't mind the fact the feeds are passed through them - but they do have the "MyBrand" service available just in case you want to still use your own RSS address.

There really is not other really good way to tell how many subscribers you have.  You could track how many times your RSS feeds were being hit by traffic - but it would be difficult to figure out.  For the Google Analytics stuff I usually just paste the code they give you into the footer of my theme so that way it gets put on every single Web page under my Web site.