I don't know about the rest, but the physics behind the ice ball does not seem right to me. The ice absorbs heat from the drink and cools it. The ice melts at a rate governed by how fast it absorbs the heat.
If the ice melts more slowly, it absorbs less heat, so it cools the drink less. You can get the ice to melt more slowly by reducing its surface area, but your drink will also be warmer.
If the ice melts more slowly, it absorbs less heat, so it cools the drink less. You can get the ice to melt more slowly by reducing its surface area, but your drink will also be warmer.