Blogger vs WordPress Blog

1. Yes, you can buy a domain name (for example, something like ldebeer.com) and then connect that to your current WordPress site. So basically, you don't really move your blog, but you add a domain name to it.

2. There are many advantages to it. Apart from adding a domain name to it (which will make it easier for people to access your site, or at least easier to remember the address), a lot of the advantages are for you, the author as well; you'll have more control over your site, basically. For a list of what you'll get when you pay for your account, go here: https://wordpress.com/pricing/