Nothing stopping you from going for a run around the terminals. All terminals except E have at least one bridge between them and another. I don't believe there is an exercise room anymore - IIRC, that was in the old First Arrivals lounge in A that became an AC. When A was renovated, that went away (sadly, the showers did too. Best showers in any airport I've experienced).

Cannot comment on the GH. Worth swinging by the front desk and asking.