You have to own the domain before you can do anything. And I haven't heard of any free email hosting providers. If you're going to be using their resources, service and support they're going to want you to pay something. Now, you could get a cheap VPS somewhere and use something like Virtualmin which is a free control panel that can help you set up your email addresses.
Hi your post is a bit confusing there are plenty of free email services
just make a email account like [email protected] buying a domain just to use as a mail service is not really cost effective