Can hot objects absorb radiation?

Answer 1

An object does not know if surrounding objects are hotter or colder than it so the proximity of other objects does not effect their behaviour.
All objects emit energy in the form of radiation provided that their temperature is above absolute zero. At absolute zero they would have no energy so could not emit.
All objects also recieve energy if they are in the path of energy radiated by another body.
Two identical objects at the same temperature would emit energy toward each other (and in every other direction) and would receive energy from each other (and from every other direction).
The amount of energy that exchanged between the two ojects would be equal in both directions so that their energy levels would be unchanged.
If one of the bodies were hotter than the other it would emit more energy than it would receive. It would get cooler and the cold body would get hotter until their temperature equalized and they would both emit the same energy to each other as they received.
The rate of energy emission is complex to calculate for anything other than a "black body" which is a perfect radiator of energy.
Follow the link for a lot more detail. You can see that Stefan-Boltzman equation only refers to the absolute temperature and not temperature difference so all bodies radiate unless at absolute zero where T = 0 so T to the power of 4 = zero and radiation equals the constant multiplied by zero.

Answer 2

Yes, they do absorb radiation.

However whether the temperature of the hot object increases will depend on whether the hot body is absorbing more radiation than it is emitting (then it would get hotter), or whether the hot body is absorbing less radiation than it is emitting (then it would get colder).

Answer 3

Objects do not absorb radiation on account of their temperature. The rate of absorption depends on the nature of the surface of the body.

Answer 4

Yes. And they also radiate.

Answer 5

yes