Can we built a website through unity.
Yes, you can. But it will work slower than regular web pages, use more internet traffic and will be able to work only on platforms that support WebGL. Not the best idea. 
yes it will work
Be sure to use asset bundles because it wont be long before you crash your ram.
also it reminds me the 2000’s era with the flash website.
But im sure it can be really interesting