Yes, it is possible to add a registration 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.
You may want to consider collecting some details at the time of the booking, and some at a later stage. For example, you could send the registration form with a link with the booking confirmation email, so that customers could fill it in, then email it to you.
You can use an online free registration form service, like: