Condensed matter (solids and liquids) and dense gases at all temperatures emit electromagnetic radiation in which a continuous distribution of several wavelengths is present, though with different intensities. What is the reason for this ?

Both 1 and 2.

All condensed matter (solids, liquids, and dense gases) emit electromagnetic radiation at all temperatures. Also, this radiation has a continuous distribution of several wavelengths with different intensities. This is caused by oscillating atoms and molecules and their interaction with the neighbours.