Is there a way to make my own notations to submissions? Also assigning an identifier or number.

I am enjoying Jotform immensely.

There are a few things I'd like to do with the submissions though.

1) Have them individually assigned a reference number or other identifier

2) be able to give them a self defined status

3) be able to add notes that can be added as a field after the submission.

1) Have them individually assigned a reference number or other identifier

It is possible to add custom unique IDs to your form submissions. Inside of this guide, you can find how to do it: 

How to Add Custom Unique IDs to your Form Submissions?

2) be able to give them a self defined status

I do not understand this question. Please explain in more details what are you trying to achieve.

3) be able to add notes that can be added as a field after the submission.

You can add a hidden field to your form and then edit your submissions and add notes to the hidden field. 

How to Hide Form Fields

How to Edit Submissions Made on Your Forms

Thanks very much. I think the answer to #3 should help with #2
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