Are supported applications available free of charge?

It depends on the application.

[WeDJ for iPhone]
You can enjoy DJing and record your performance free of charge when using the DDJ-200.

[rekordbox]
You can enjoy DJing and record your performance free of charge when using the DDJ-200.
You can purchase additional features as well.

Subscription or In-App purchase is required for djay and edjing Mix if you want to use additional features after installation.
Refer to the website of each app for details of features and subscription as well as cancellation procedure.