Interesting requirement - Square has a lot of features and options but, I'm thinking you need a solution that's outside the box. Square does have a Developer Forum, you could check there to see if anyone there has some thoughts. It would take quite a bit of custom coding to be able to transfer data from the custom fields when they book to the form you plan to complete and then have them sign it. A work around would be to use a Form Creation App like Jotform - this work around would be outside of Square. Jotform can use Square to process transactions, something to keep in mind for future ideas. As for how you plan to get the form to the customer (i.e., email or in person), that was not mentioned. Besides email and in person, the form could be stored in the cloud (think Dropbox, Google or Microsoft), from there you could send the customer a link or URL. (From personal experience, I've tinkered with Jotform - there's a ton of templates that can be used as is or customized or you can start from scratch.)
