Is it possible to insert Splunk dashboard into some third party software, but only dashboard UI, without Splunk 'header' (which contains Splunk UI navigation, different menus, etc) ?
Yes it is, but it's not very secure..
Take a look at http://www.splunk.com/base/Documentation/4.2.2/Developer/3rdParty.
Are there any updates to this topic? I notice the docs mention. "For security reasons, you should implement this feature using SSO." Any examples?
Embedding option is currently available in version 6.1 and higher.