CB has nothing to do with your sites URL. You'll need to contact your host and buy a new domain name if you want to change that. As for routing the old to the new you'd point your old domain to the new domain, which your host should be able to help you with as well or whoever you registered your domain name with. As for ecommerce we provide a subscription management system shown below.
www.joomlapolis.com/addons/cb-paid-subscriptions
You can demo CB Paid Subscriptions on our below demo site as well.
demo.cbdemosites.com/