A domain costs about $10 a year - if you care about your site, or if it hase any value at all, then buy a real domain - the cost is minuscule.
"Free" hosting is readily available if you can put up with the ads (shop around, some hosts are more intrusive than others). Most, if not all, will provide a free subdomain.
I do recall one company giving free domain names but they simply put the site in a frameset with their own ads in the other frame. IIRC they dropped that offer a couple of years ago.
PAYG cards can be expensive but they are a good way for minors to get access to any aspect of ecommerce.