The water creates a better way to transfer heat from the container to the freezer because it has direct contact with the container and replaces the air around it. Yes the water needs to be cooled too, but still the process is way faster because air really is a good insulator for heat. This is why insulating materials for houses e.g. always try to maximize air content (foam, glass wool, styrofoam)
Correct. Convection would just annihilate your insulating effect