Liquid nitrogen is -196˚C and quickly freezes the ingredients into ice cream. The nitrogen boils out leaving deliciously creamy ice cream. The “fog” that we see is condensed water vapor though, not nitrogen gas.
Water has a very high surface tension because of the strong hydrogen bonding between water molecules, which allows the pepper to float on top of the water. When a small amount of soap is added it forms a monolayer on the surface. The monolayer spreads away from the point of contact causing the pepper to move to the edges of the dish.