How to create a support request (Case) via API?

We've been building out API data flows into Creatio including automated order/invoice creation from cart data and webinar registrations from our website. We are now creating a support request form on a website that should create a case linked to a matching contact in the CRM. 

Retrieving the contact ID isn't a problem, but we're stuck trying to figure out how to create the new Case. We can query the /Case endpoint and see existing case data. How do we POST a new case?

And will we be able to take  file uploads from the webform and submit them into the /CaseFile object? Or will it have to a linked reference like a URL?

Thanks in advance!