Download can be straightforward. If you use a web embed to display it, there’s a built-in button to do so.
To email the PDF, you would need to use Make/Zapier. Pass the link of the PDF to Make/Zapier, have a step to download it (in Make you’d use the HTTP module), and assign it as an attachment in the email module.
In the past i have also used “Open link” action using the pdf file url and it automatically downloads it. This is useful for when you dont have the paid plans because Web Embed is not available for the FREE plan. This is just to add more information to what has already been shared in case the next person does not have a paid plan.