When I am creating a web application and selecting to create a new IIS site and new application pool in IIS, it does not create both. However web application gets created, I was also able to create site collection under it but when I am trying to open a site collection it says "page can not be displayed". Not sure what is going wrong. Using sharepoint 2013.
when you says its created, did you see the webapplication in IIS or From Central Admin > Manager WebApplication?
did you try to create the webapplication using the Powershell? here is technet code for this, try this http://gallery.technet.microsoft.com/Create-SharePoint-Web-742a8fb9.
also check this blog for the time out issue, you need to make changes to defaulapp pool.