If you had water that was for example at 105C, you're stating it would stay at 105C as it boils? And that the boiling would not lead to a decrease in the temperature?

When you add salt to ice+water the temperature decreases. Your misconception is that somehow energy is being removed from the system.

This is not true. You can do the kitchen experiment yourself.

No the melting is endothermic.

>just adding salt can't take energy out of the system

The temperature decreasing does not mean that the total energy of the system has changed. There is an energy transfer between kinetic energy and potential within the system.

Only really in an ideal gas system does the temperature relate to the total energy.

Energy is conserved. The thermal, kinetic energy of the ice and water is transferred to the potential energy in the bonds of the ice (to break them).

The temperature of a system is only ever directly related to the total energy of a system for an ideal gas.

Ice in equilibrium with (pure) water will stay at 0 degrees C. No higher and no lower. If you add salt to the water, the equilibrium temperature will decrease. So a brine ice mixture can be lowered below 0 degrees C. This lower temperature system would "stay cool longer" because it is colder.

>It's as if they're saying that by adding salt, they've removed even more energy (heat) from the mass

Melting is an endothermic process. This process will "remove" heat via bond breaking in the ice. So by adding salt to the water and lowering the equilibrium temperature, the system will respond by melting some of the ice. This consumes energy and lowers the temperature until equilibrium temperature is reached.

EDIT: To clarify a misconception, an observed decrease in temperature does not equate to the "removal of energy from the system" (when simply adding salt). A decrease in temperature can occur when there is a transfer of kinetic energy to potential (when ice melts endothermically). Regardless, in the water-ice system the temperature is not actually proportional to kinetic energy. That is only the case in an ideal gas.

Thermal cameras aren't that great at accurately measuring temperature particularly when comparing different materials. The emissivity of the metal with be very different to that of the other materials and so a different temperature will be measured.

If a bound electron is photoemitted the “extra” energy becomes the energy of the free electron. Free particles don’t have quantised states.