Theory:

     Again I heard that sound from above.
 
5. I took a close look at my face in the mirror. I made an important decision — I would shave daily and grow a thin moustache to look more handsome. I was after all a bachelor, and a doctor!
 
     I looked into the mirror and smiled. It was an attractive smile. I made another earth-shaking decision. I would always keep that attractive smile on my face ... to look more handsome. I was after all a bachelor, and a doctor too on top of it!
 
     Again came that noise from above.
Explanation:
 
When the doctor was combing his hair, he heard the same noise from above in his room. It was the second time the doctor had heard the same noise, but he had dismissed it as the result of the rats in his room. He then shifted his attention to the mirror, and it was about this time that he made the decision to shave every day and grow a thin moustache, believing that this would improve his appearance.
 
He told himself that he was a bachelor and a doctor, which meant he had to appear presentable in front of others. When patients see their doctor with a pleasant face and a presentable appearance, they might feel better and have more confidence that they will be healed of their illness. Furthermore, the doctor emphasises the word 'bachelor' since, as an unmarried man, he thought he needed to appear more attractive and handsome in order to acquire a better partner.
 
He smiled at himself in the mirror and complimented himself on his attractive smile. And he made another 'earth-shaking (important)' choice based on it, as he was determined to constantly smile in order to appear more attractive. Despite the fact that the doctor had pulled out his book and sat down at the table to read it, his urge to look at his appearance in the mirror diverted him.
 
The doctor continued thinking about different methods to make himself appear more attractive and better while looking in the large mirror. The doctor repeats himself, "I was single and a doctor," which displays the doctor's sense of humour as how he believes 'beauty' to be a mandatory thing for an unmarried person, and that too, for someone who is a doctor by profession. This also implies the doctor's arrogance in being a doctor.
 
The doctor then heard the same noise from above for the third time. Even the third time, he ignored the sounds, oblivious to the danger. He was unconcerned by the noise from above and returned his attention to his reflection in the mirror. This also serves as a hint to the readers that the large mirror was extremely enticing, causing the doctor to become inattentive.
 
Meaning of difficult words:
 
S.No
Words
Meaning 
 1.
Moustache
A line hair that grows on men's upper lip
Reference:
National Council of Educational Research and Training (2006). Beehive. The Snake and the Mirror - Vaikom Muhammad Basheer (pp.56-60). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.