Yes, it is possible to add an intake form or questionnaire to the booking page, with questions and fields, using customer custom fields. Click here for more information on how to set up custom fields.
However, please note that if your registration form is too long, the customer could take a long time to complete the booking. When customers try to make a booking online, Bookeo will hold the seat for 10 minutes.
Consider collecting some information at the time of booking and the rest later. For instance, you could include a link to the registration form in the booking confirmation email, allowing customers to complete it and send it back to you separately
You can use an online free registration form service, like: