Murad: You can use a web hosting service such as Go Daddy and pay for a server and domain name or you could go with FREE web host such as byet Internet Services like I use. You get a FREE FTP account with PHP support and it doesn't rely on HTML templates so you can upload your own HTML web designs and register a free domain name.
You can use GitHub.com to hold your own html web pages.
Your question doesn't really make sense. If you want to create a website, then you don't need a "free website" just create the website on your local machine.
You cannot redesign a website you do not own! There are many sites that you can post to, but modifying the design of a site you do not own, to you own design, none that I am aware of. Why would someone design their site so you could just hijack it?