Yelp Home Page

Hi, I want to do something like “Yelp” to which the home page does not have a header and have a search bar in the middle of the page with the logo.

I would like to seek help to see how I can:
– hide the header section in home page only?
– how do I add a search bar in the middle of the page with an image behind like attached pics? and default header in other pages.
– options in the search box or available categories.

Thanks in Advance.