In order for the site to be publicly accessible you need to host the site on a server that is publicly accessible. Your local MAMP server is almost certainly not public. There are hacks and workarounds that would let you host the site from there, but don’t. Lease a server and install your site there. You can try one of these.
You don’t technically have to have a domain name to host a site. You can host directly from an IP address, but you probably want to lease a name as well.
Your site has nothing to do with wordpress.com. Your password, your domain name, all different.
As far as the Site Address setting, ‘localhost’ means “this computer”. That setting only works if the browser accessing the site is on the same machine as the server, which works for your test environment I suppose. It won’t work for a hosted site, nor will it work if you want to visit the site from another of your own computers– we all about six or seven right? 🙂 When you get a public server and a domain name, use that domain name– http://mygreatsite.com/wordpress
Work locally using your MAMP install, FTP the PHP/CSS/Javascript to the hosted site. Add actual content on the hosted site or you have an issue with having to convert URLs when you move the site.