If we're in a physics simulation, we don't experience at the rate that the simulation is processed. One "tick" of the simulation could be processed in one second of the host universe, or one hour: and we wouldn't feel the difference. We are processed at the same tickrate as the rest of the universe, so we experience the passage of time at the same rate that the simulation flows.

The speed of light isn't just the speed of light, it's the speed of causality. It just so happens that light moves pretty well at that "speed limit" (in a vacuum). We could ask our computational hosts to increase or decrease c, and we still wouldn't be able to travel any faster than it.