Do I need to sign up for a rekordbox plan or buy a Serato DJ Pro Expansion Pack to use DVS with the DJM-S7

The DJM-S7 is a Hardware Unlock device for rekordbox, so you can use a range of features in Performance mode for free while your computer is connected to the mixer. You can also use Serato DJ Pro for free.
To use additional features in either application, you'll need to subscribe to the relevant rekordbox plan or buy the relevant Serato DJ Pro Expansion Pack(s).
Find details on the features available in rekordbox via Hardware Unlock [here].
Find details on features available in Serato DJ Pro [here].