So, is it not possible for so much big polymer molecules in our body like DNA to absorb Radiowaves and heat up and to damage our body. (If this is not the case. Other than this also, do Radiowaves harm us or not?)
Yes, the heating effect on human tissue is possible and dangerous if the EM field is too strong. This has nothing to do with DNA mutations or ionization.
Such harmful EM field can be present near FM radio emitter antennas (VHF, very short waves) or radars (microwaves), for example. These devices are unfortunately sometimes approached by human workers even while emitting strong radiation. If a worker gets too close, he may get exposed to dangerous intensity of radiation get harmed by thermal effects of the radiation.
One of the most easily acquired harm is cataracts in eyes since they lack an efficient cooling mechanism. If the radiation is strong enough, skin/organ burns can occur.
According to http://www.arrl.org/rf-radiation-and-electromagnetic-field-safety :
At frequencies near the body's natural resonant frequency, RF energy is absorbed more efficiently, and maximum heating occurs. In adults, this frequency usually is about 35 MHz if the person is grounded, and about 70 MHz if the person's body is insulated from the ground. Also, body parts may be resonant; the adult head, for example is resonant around 400 MHz, while a baby's smaller head resonates near 700 MHz. Body size thus determines the frequency at which most RF energy is absorbed.
In populated areas, radiation due to radio transmitters or radars should be low enough to not cause such harmful thermal effects.