How to update form record data

I have the ID of a record, but unsure which API to use to update that form record.

Suggestions?

Forms generally aren't edited after they are submitted. There is a "form cleaning" workflow documented here, which comes with a number of caveats, but I don't believe there's a corresponding API.

Does this form modify a case? Some projects will submit a "correction" form to fix properties set incorrectly in a previous submission.

Ok, is there an API to submit a new form record?

Yes, that API is documented here.