Hi Damian,
Thank you for interested in Document Indexer extension, regarding to your questions, i would like to answer as below
1. Document Indexer supports all Joomla Search functions, the search function you mention is Normal Joomla Search, and Document Indexer supports it.
2. Document Indexer doesn't index new files automatically, in documents list, we have button on the toolbar which allow you to index "new" documents.
Thanks
Dam