Is it possible to have a serial number for the submissions?

Besides that, is it possible to have already a running serial number for all the forms that are submitted?

What serial number are you referring to? We have a unique number that you can assign to your form submissions. I think this is what you are asking. Please check then let us know if not. Here's the guide:

https://www.jotform.com/help/79-Add-Custom-Unique-IDs-to-your-Form-Submissions