In order: no, pressure, and no. As long as the container is not changing shape, size, pressure or temperature, no work is being done. Or, to be more clear: no net work is being done. For every unit of energy transferred from the gas to the container, an equal amount is transferred from the container to the gas. If that wasn’t the case, it by definition wouldn’t be at equilibrium - at least one of pressure, volume or temperature would be changing.
