Here are the answers to the questions:
1. The mother asked her son to avoid the kid with cough because cough can spread communicable diseases like cold, flu, tuberculosis, etc. from one person to another.
2. The mother let her son play with the kid with asthma because asthma is a non-communicable disease. It cannot spread from one person to another. Asthma is caused due to inflammation in the airways of lungs and cannot be transmitted.