Yes. The Tumbler fits upside-down inside the Teacup. This pair can then be stacked on top of another pair.
Yes. Though the polished inside surface makes them very easy to clean with a sponge or dish cloth. Who wants to wait for the dishwasher when there are spills to save?
The Tumbler and Teacup are made from recyclable food-grade polypropylene. It is a standard material for the food industry and is tested for all sorts of cooties like phthalates and lead.