Regarding your issue, I've checked your site and seems like there is some issue on your previous data migration from your JomSocial into EasySocial I've fixed the data and now the advanced search on names should work correctly
Regarding your toolbar search, I've purged your smart search indexed items and then re-run the indexing process and now the search is working correctly http://screencast.com/t/Z12Gmv65
Also, when I trying to search using dating search with 2 paramaters Name and Age it displays users with different names
As for the above, I've added a fix on your site and can you give it a try again? The fix will be added into next release of EasySocial