I created a wordpress site with their template. In order to host my wordpress site on another hosting platform, I need the source code for my wordpress.com site. (that contains
So the answer above is correct but that probably doesn't help you. What you can do is follow this link: http://www.siteground.com/tutorials/wordpress/transfer-wordpress/
It basically shows you how to migrate the data. You will need to setup wordpress.org on your new location first then once both are up, you can export from wordpress.com to your new location using I think a migration wordpress plugin. This should bring over your database. You will need to figure out how to migrate the template and style (look and feel) of the site. You may want to just find a new template that you like because I don't know how compatible wordpress.com templates are.
Hope this helps.
if you want to download a theme, you can find said theme on wordpress.org. If the theme is listed as premium, you'll have to buy it.
if you want to change yourDomain.wordpress.com to yourdomain.com please read this page.
WordPress.com uses a modified version of the code available at https://wordpress.org/. You can't download their modified version, but you can download WordPress.org and start from there.