How to Set up Search for Extended Web applications Sp2013

Couple of things to be noted.

1. Extending a web app does not mean you get separate content, extended web application share same content database as Default Web Application.
2. Extending Web application basically used where you want to implement different authentication to a different set of users. I.e you want claims windows on default zone and for intranet zone you want o implement ADFS.
3. When you extend a web application, you expose the same content to different sets of users by using an additional IIS web site to host the same content.
4. Search crawls only windows authentication based web application.

Now you saying not all the content crawling? what that mean...did you check the Crawl Logs for any possible error?

Check this blog for more information: http://sharepointobservations.wordpress.com/2013/08/06/sharepoint-2013-configuring-search-to-crawl-web-applications-using-claims-and-adfs-2-0/