Can a user save a pdf of the form they complete

Yes, this is indeed possible to do. 

You can add a print button, so your users will be able to print the form with the info they've entered before to submit it, to do it, open your form in the Form Builder, click on the submit button, on the top toolbar you will find the option to show the print button on the form. 

The second option is attaching the PDF on an email auto-responder, to do it first open the email wizard: 

Once there go to the email auto-responder and click on the "Edit" button: 

Here you have two options to provide the PDF report with the submitted data, the first one is including the link to the PDF in the email, to do it click on the "Form Fields" option and there you will find the "PDF Link" option: 

The second way to do it will be going to the "Advanced" tab and turning on the option to attach the PDF file on the email: 

If you have any question, please let us know.