Hi Nivedita, 

I would suggest cloning the OOB widgets ("Welcome Banner (CD)" and your header) and using those cloned versions on your pages instead.  For putting the search within that welcome banner, you will update the widget to call the OOB typeahead search widget.  Removing the search from the header, this is generally on the header from your Theme. I would also recommend you consider the usability of ESC without the typeahead search on each page via the header before removing it.  If you are driving your users to search, it is nice to always have the search bar on each page they navigate to.