Hello Daniela,
here my answers:
1.
Q: I would like to know if it is possible to manage free bookings.
A: Yes, it is possible to offer seats for free.
2.
Q: Also (for group bookings), I would like to know if it is possible to set a maximum number of bookings per group (example 4).
A: I don't know exacly, what you mean with "group bookings". But you can set minimum and maximum players for a court. see screenshot
3.
Q: I would also like to know if it is possible - in the booking form - to enter the fields to specify the names of the group members and to have custom fields
A.: Yes, see screenshot. but note: the number of the fields for the names of the players is fixed (you decide how many), it doesn't depend on the number of players who are registered.
Q: My requirement is to manage time slots with up to 30/35 seats, divided into small groups
A: you can manage this by the price groups. An example see the screenshot.
Sigrid