If cans of soda or place in the chest full of ice, does the coldness from the ice go into the soda or does the heat from the soda go onto the ice?

The coldness from the ice transfers to the soda, causing it to cool down. Heat from the soda does not transfer onto the ice. Heat always moves from higher temperature objects to lower temperature objects, so in this case, the heat from the soda would not transfer to the ice because the ice is colder than the soda.

Which of the following would be the best at transferring thermal energy A fiberglass insulation B Styrofoam cup, C rubber floor mat, or D iron radiator

Iron radiator would be the best at transferring thermal energy because metals are generally good thermal conductors compared to insulating materials like fiberglass, Styrofoam, or rubber. Iron radiators are designed to transfer heat efficiently in heating systems.