Can the advanced search interface be used to search for answered threads. (I know there is display of some unanswered threads on the forum pages and in advanced search there a way to search for threads with the most replies. )
I don't know whether I fully understand what you are asking. In the advanced search page, there is an option "Minimum number of replies". If you want only answered threads, you can increase this to 1. On the other hand, for unanswered threads, you can keep the number as it is, but when the results are displayed, you can sort them by number of replies in ascending order. That will bring up the unanswered threads to the top.
As of now, there is no "Maximum number of replies" option which can bring up only unanswered threads.
You can check the "Display results as threads" option at the bottom of the page.