Should I use hot or cold water?

Yes, the hot chocolate increases the temperature of your mouth, making it more sensitive to colder temperatures, for instance the air.

It will cool slower, as the metal in the cup will conduct the heat and keep it warmer longer.

Yes, but make sure the milk does not tip or spill out and no water gets in.

Boil the brine to dissolve the salt, and pour it over the pickles while still hot.

I don't think you should use a cast iron pan but it could work if you are desperate. I would definitely use a gas stove.

Hot water.

Air in the pipes makes them bang.