Can you just email a link to a form for completion and can you manually add responses from paper forms?

Yes, you can certain do both of those with your forms if you wish. You can email your form using either its direct link or you can use the embed option to email it from your JotForm Account.

Option A -

Option B -

I apologize about that as I realized I didn't go into much detail about it. Anyhow, I also meant to say that in addition to that your paper responses you would have to go into your form and manually fill in the paper information and then submit it to yourself.