I have a pre-made Google Sheet which has cells to be marked as "pass" or "fail" depending on the person's score. Is it possible to link a Form response to record a pass or fail mark depending on the scores of each person? Sorry if this is not making sense I can elaborate if needed to.
Contrary to what many believe, it is actually possible.
When you edit your form, at the very bottom there's a checkbox where you can allow editing of submitted response:
If you use a newer version of the Google Forms, you can click on the Gear icon on the top right and see the following page:
Now, what you need to do is manually submit score for each student. After every submission, you will be offered a link to edit the submission. You need to manually copy and save each link to allow future editing.
If you want to automatically record the edit response link, you can do so via Google Apps Script.
It is not possible to link a new Google Form to an existing Google Sheet without utilising Apps Script.
Your next-best option would probably be to incorporate the formulae you have in the existing spreadsheet into the spreadsheet that is generated when you create the form. Each question in the form gets its own column, but you can add your own, additional columns of cells that, respectively, compute scores and mark down a "pass" or "fail."