Question 1 and 2
Q.1. Why does taking antibiotics does not reduce the severity or the duration of the disease if we have a common cold ?
Q.2. Why do doctors sometimes prescribe antibiotics when we have a viral cold?

1. Antibiotics act by blocking certain biochemical pathways which are essential for the survival of bacteria like cell wall formation, protein synthesis etc. It blocks the formation of cell wall in bacteria, which makes bacteria weak and ultimately results in death of bacteria.  However, antibiotics cannot be used against viruses and cold is a viral infection. This is why antibiotics do not reduce the duration and severity of common cold which is caused by viruses.
Viruses do not possess any cellular machinery of their own to function. They are non-living outside the host and they have very few biochemical pathways of their own. Hence, it is difficult to find virus-specific targets. Therefore, the antibiotics are not effective against viral infections. 

2. In certain cases, common cold can progress and cause bacterial infections. So, to combat the effects of this infection, antibiotics are prescribed by the doctor.