I heard that the electric company would upgrade your main breaker to a 200amp for free. Is this true? If so, I wonder if they would upgrade my sub-panel box also that is located right beside the main breaker panel. I was also wanting to ask, would I need to run a ground rod beside my breaker panel outside my shop that I will be wiring up here shortly even if my main breaker panel already has one ran?

The utility company will do NOTHING inside the house. In rarew cases they will provide up to and including the meter pan, but most stop their responsibility at the connections at the top of the house.
A service upgrade is solely the responsibility of the homeowner.