Is it possible to develop a website without buying domain and hosting ?

Yes it's possible to make a website but if you want that your website reach to more people so you have to buy a domain and hosting server.

Use https://zeit.co

There are free services that allows one to host static websites such as surge, github pages, netlify, now. You can use any one.

Gee thanks! :)

What I meant is can the developer create his own domain and hosting ?