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.
When M&M’s are placed in water, the outer shell, which is made of sugar, dissolves. The sugar moves from a place of high concentration (the M&M) to a place of low concentration (the water away from the M&M). When the sugar shell dissolves and moves outward, it takes the layer of food dye with it. When more than one M&M is placed into a petri dish the colors do not mix because the concentration of sugar at the interface is approximately the same. Also, around the bottom of the M&M water appears cloudy because the sugar that is dissolved is more dense than the water, so it sinks.