You can do all of that with Fillout’s advanced forms for Airtable.
Fillout lets you create 2 types of forms: a form to create Airtable records, and a form to update Airtable records
After the user creates the record in Airtable (with the create form), you would have an Airtable automation send them the link to their unique URL (which is the update form).
Fillout also has the ability to create a PDF of the form responses, which the user could print.
— ScottWorld, Expert Airtable Consultant