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There are many formats you can use do document controls. An easy one to start with could be this (in a spreadsheet):
Down the left column you would list your controls and number them. You could also group them by Principal Business Activity (PBA).
Across the top, list your control objectives. You’ve now created a matrix. You can ‘X’ the box under the objective that each control satisfies. After listing all the objectives, you could then continue with columns for Primary v. Compensating, Preventative v. Detective, Automated v. Manual, and then your six financial statement assertions. Again, this would be a very basic control list, but a starting point for you. Lots of other formats could be just as appropriate.
For your second question, I would argue that if none of the assertions apply, then it’s probably not a SOX control. So yes, they should be documented.