To answer your questions as below:
1. How to verify if the summons is genuine, if the ecourts website does not show to which court the matter is allocated even after 1 month?
Cases are often transferred between courts and ecourts is sometimes not updated to the latest case status as it depends from court to court. Also if you are able to see your name as the accused/party, then the summons must be genuine as it should bear the seal and signature of the magistrate and court (you will also find a number associated with the summons issued)
2. Does the metropolitan magistrate court in Kolkata have jurisdiction in this matter if the accused is residing outside its territorial jurisdiction?
Any court in India can summon any person from anywhere in India as long as the court is satisfied and admitted a complaint.
3. Should I prepare to take bail as the 1st step before I am given an opportunity to argue my case?
You do not need to apply for bail as it is in the summons stage. The court has not yet issued a warrant.
4. Can my lawyer represent me without my physical presence on the date of the summons and answer the charges on my behalf and question the jurisdiction?
Yes, your lawyer can represent you even in your absence. Also can apply before the court to exempt you from physical appearance on further dates. You are advised to engage a lawyer in Kolkata who should be able to guide further.
5. Can I give power of attorney to another person to represent me and be physically present on my behalf if I do not want to go?
Your lawyer himself should be able to represent you in the case and you can also provide power of attorney to anyone who is aware of the facts to represent you in case your appearance is instructed by the court during any stage of the trial process
6. Since, they have asked me to appear in person or through a pleader in the summons , does it mean I need not be physically present if my pleader or advocate is present?
Answered in #4 so as long as a pleader represents you, you may not be present in person.
7. Normally how long does it take for the e courts website to update the exact status?
It is generally within a day or two, if it is updated all.
8. Is it possible that Bajaj finance advocates are issuing the summons in connivance with lower staff without the matter getting allocated to any magistrate just to intimidate me?
Very unlikely as it would amount to fraud and impersonation and no court staff would ever do that.