Yes, that's how you do it. Plus there are many other analytics services out there - you should try them too while you are updating your code!
as long the pages are on the same domain anyway. All pages on your site should be tagged with the GA code (within the <body> </body> tags) to be able to get useful information from Google Analytics.
It's common to place the code within the <body> section, however, you can get more accurate data by installing your favorite tracker within the <head> section - especially if you have a heavy site with many elements. (Some slow connections or unstable browsers can timeout or interrupt the transmission of the later elements. In some cases, people will navigate on before the tracker has loaded and counted their visit/page view)
Accepted, but the recommendation from Google is to setup within the <body> tags. I have seen it working fine in the <head> tags but placing the code at the bottom of the page ensures that if there is an error with the script that your page will load correctly before encountering the error. I'd go with allowing users to see the page over ensuring I see a page view in Analytics.