The continuous crawl on works on SP2013 content and shall display content in the crawl results as soon as it is indexed ( it doesn't wait for the crawl to complete). It is a good idea to run incremental crawls as they index more data than just SP2013 data and continuous crawl does not process or retry items that return errors and the incremental crawl shall clean theses items up.

Internet users are external users and normally access the servers using anonymous access - they do not need CALs. You can do this on the SQL Server and the WFE's to check the correct versions and features are being used.

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