2. Which state of matter—solid, liquid, or gas—is the best at conducting heat? Why?
Typically metals such as copper and aluminum are preferred to conduct heat. In metals the electrons are shared and form an 'electron cloud' that typically moves at tremoundous speeds and are good at moving energy from a to b. Metals are also composed of a crystalline structure, can be seen under a microscope, and vibrations between the crystals conducts heat as well. However, condensing a vapor on a surface i.e. going from a vapor to a liquid can exchange tremoundous amounts of heat as well. Typically, most powerplants involve heat exchangers that conduct heat through solid, liquid, and gas states via pipes. Therefore liquid, solid, and gas interchange of heat are necessary, and the conductivity off all three must be taken into account. Also, radiation heat exchange at high temperatures can significatly greater than the interchange between solid, liquid, or gas. If this interest you look into mechanical engineering.
Gas. because gas molecules are produced by heat and gas's are hotter and they expand more and move a lot more faster so it allows heat to transfer more.