Web design project guidance

Is it necessary to make projects based on given user stories or we can design with our own style ??

This is your education and you can choose which aspects of FCC you want to use. I will say, however, that learning how to build a project based on user stories is very important professional skill. If you really want the best of both worlds, this is what I would suggest: complete the FCC projects based on the user stories, then fork your own project and keep working on them based on your own requirements.