Is there a way to get the print version (pdf) of a submission sent through (attached) with the notification email?

Yes, under the advanced tab you can enable the "PDF attachment" option which will include the PDF report of the submission, here is a guide about the email notification settings: https://www.jotform.com/help/25-Setting-up-Email-Notifications 

You may also edit the PDF report, this guide will help you doing so: https://www.jotform.com/help/384-How-to-Customize-PDF-Submissions-Report 

If you have questions, let us know. 

If you click PDF under the advanced tab, you have to select a PDF to use. I want to select the print version PDF that you get from the inbox (that is downloadable) after a submission is made. Is this possible? 

Unfortunately, the only PDF document that can be attached to the email is the one from the PDF editor, you may customize it if needed with the guide provided above. 

Okay, after I am done customizing it, will signatures from the form show up on the attached PDF that comes in the email? 

Yes, all the content from the form can be actually included in the PDF report.