The default search implementation doesn't seem to search custom fields and DataObjects associated with a page? Is it possible to change this functionality? I want the user to be able to search ALL content on all pages.
Yes, unfortunately the default search doesn't extend to DataObjects. The main two choices in SS3 are Solr and Sphinx. I haven't used Sphinx but Solr is excellent - you can get the latest version here:
It takes a bit to set up, but well worth it.