You are not required to submit them at all, they are just nice to have.
A reference letter which states how much you were paid is a strict requirement.
But there's a lot of discretion here. There might be more leniency in your case. So no harm in trying to apply earlier not meeting all the requirements.
Who qualifies
With certain exceptions, to qualify for OHIP, you must meet all of the minimum qualifications listed below plus at least 1 of the additional requirements.
To meet the minimum qualifications you must:
be physically in Ontario for 153 days in any 12‑month period
be physically in...
It depends on a decision maker. Most often you get an update and/or a decision on your reconsideration request. Sometimes IRCC just reopens your application and makes a decision again. Not always a positive one.
No, you don't need to to update your proof of funds. But there's a slight chance that IRCC might request an updated proof of funds, just be prepared.
No action required from you now if not requested by IRCC.