Your SharePoint site has 2 sides to it
You have your Public facing site. This is just an external template base website. You can build your brand or whatever you want, but its external facing and no login required to see it. You can CNAME your custom domain to go to this, like www.whatever.com, or sharepoint.whatever.com or sp.whatever.com - You get the point.
The other side is the "intranet" or "internal" SharePoint site.
This site is used as your main SharePoint site. Your URL will be whatever.sharepoint.com (whatever = yourdomainname)
Users can login to that URL with there licensed account and get into SharePoint, they can also just go to portal.microsoftonline.com and click "Sites" and get there too.
With the internal share point site, you can invite up to 50 external users for free. This means if you make a site for your customers, you can invite them to share information on one of the sites and they just sign in with the Microsoft Live ID email address.
So, hope this helps
Yes, its all accessible from the externally (there is no other way, its not located in your office)
You can also turn on Guest links, which means you can share a document with an external user and they are not required to sign in.