No, you can use this Lingo3G demo free of charge. License fees are required when deploying Lingo3G on your own servers or workstations, either standalone or integrated with your application.
Please note though that this demo imposes daily usage quotas to avoid abusive use of the free service. The quotas should not affect reasonable use of the application.
Yes, the source code of this demo application is available as part of the Carrot2 framework under the Apache Software License 2.0. This means you can freely reuse this application, along with Carrot2 clustering algorithms, for your open source or commercial projects.
Please note, however, that the source code of parts of this application is not available. In particular, the Lingo3G clustering algorithm, FoamTree treemap and Circles pie-chart are proprietary commercial offerings and come only as binary distributions.