Electromagnetic waves are formed due to simultaneous oscillations in electric and magnetic field (both are perpendicular to each other and perpendicular to the propagation of the em wave). Both electric and magnetic fields can exist in a vacuum and do not need a material medium to exist or oscillate. So an electromagnetic wave can propagate without a medium.
These radiations carry energy with them, so when a body releases radiation it loses energy, which manifests into a temperature loss. When radiation (energy) is absorbed, the body gains energy which is manifested in the form of a temperature gain. This is basically a heat transfer with radiation.
Both statement 1 and Statement 2 are true, but Statement -2 is not the correct explanation for Staement -1.