Does radiation cause a change in temperature? If yes, then is there a limit to the temperature decrease? If no, then can the body which radiates heat attain an absolute zero temperature?
 A: Yes, radiation can cause a change in temperature. It's a form of heat transfer, after all. Radiative heat transfer can cause an object to warm up or cool off.
The Earth's temperature hasn't changed all that much over the last several million years. (Global warming and ice ages represent smallish temperature changes.) This means the Earth is more or less in balance, with just about as much energy coming in from the Sun as is going out via thermal radiation, and all of that heat transfer (both directions) is radiative.
There is a lower limit for large objects, and that's the 2.725 kelvins cosmic microwave background radiation. A large object in empty space will eventually come into equilibrium with that radiation, and that equilibrium point will be 2.725 kelvins (currently). Small objects (sub-millimeter) have a harder time interacting with microwaves, so they can cool below the CMBR temperature.
A: Radiation obviously causes a change in temperature. Sit in front of a fire for a while.
The upper limit of the decrease in temperature is the temperature of the cold source which is acting as the counterpart.
A body which only radiates heat could only attain absolute zero if heat were being pumped out of it somehow and concentrated elsewhere - it would not automatically reach absolute zero, because the cold source would heat up from absolute zero.
A: Everything is gaining and losing heat all the time, partly by radiation, and partly by other processes, such as conduction.  The temperature of an object changes until all of these heat fluxes sum to zero, at which point it is in equilibrium and the temperature remains constant.  If you could put an object in an infinitely large, utterly empty space, so that there was no radiation produced by anything but the object, then yes, it would radiate its energy away.  But there is no infinite empty room.  Even in outer space there is cosmic background radiation, so the object would never drop much below 3 K even there.  At that point, it would be gaining heat from absorbed radiation as fast as it lost it from emitted radiation.
A: A basic observational law of physics is that all bodies made up by atoms and molecules, from gases to plasmas, radiate electromagnetic energy with a spectrum dependent on the temperature, called black body radiation.
It is called the Planck radiation formula for a black body:

Note that it is a function of temperature , and a whole spectrum from infrared to gamma rays is radiated , with temperature identifying the spectrum:

When several bodies are in an isolated system, they come to a thermodynamic equilibrium, at the same temperature T, the hot bodies losing energy in the form of radiation and the cold ones acquiring it.

If no, then can the body which radiates heat attain an absolute zero temperature?

In our universe the coldest black body is the cosmic microwave background radiation in outer space, which has the best fit to the Planck formula.
This spectrum is of a temperature 2.7260±0.0013K  and this is the closest a material body can approach 0K if in equilibrium with space. 
