You are liable to pay the society dues failing which flat would not be transferred in your name in society records 

It is for you to check no due with society. Bank auctions the property on as in where in basis. Only threes years amount can be claim that also by lower interest rate and through court only.

Liabilities come with the owner.  Your society is not responsible to collect the arrear from previous owner. 

You pay the arrear and recover it from the previous owner who is liable to clear all his dues.  

Issue a notice to him to this effect. Give some time to repay. In default file a money recovery suit against him in civil court. 

1. Yes, you aren't liable to pay any arrears maintenance of previous member. As the flat was auctioned, the society should have claimed from the auctioning bank, not you. 
2. Now, the society is legally duty bound to do all formalities to include you, the rightful owner, as new member. Any claim of arreas maintenance of previous member is blatantly illegal. 
3. If the society doesn't include you as member (by issuing NOC etc) then you must take legal action by moving the cooperative court. 
4. You obviously require the service of an experienced counsel. I'm prepared to handle your case deligently. However, I require an exhaustive consultation session with you first. I'm based in Navi Mumbai/Mumbai just as you are; so it shouldn't be much difficult for you to visit me for exhaustive consultation.

You are not liable to pay the old dues. The society and bank are responsible to recover from old member. If they don't give membership complaint to dy registrar. 

- Since, you have purchased the said flat on the basis of e auction by the bank , then it was duty of bank to recover all the amount from the defaulter.

- Further , for the arrear , Society is also responsible for the same, Because it was their duty to inform the bank for the said default , and further the society was bond to serve notice to the defaulter as well for the arrears.

- Better issue legal notice to the Bank for the said payment and also serve the same with the society .

- As per law , you are not responsible for the arrear of previous owner , It is the bank who transfered the ownership with consideration to you.

See society can recover the amount though it was your duty to ask bank before purchase or further now you have to recover same from bank as you have liability  only to pay after the date of the purchase. 

check the public notice which invited people to participate in e-auction 

it must be issued on 'as is where is and what is there basis'

which means it is for the bidder to make all inquiries regarding the flat put up in auction to ascertain about any pending dues and outgoings in respect of that flat which is due and payable to society and other authorities

since you seem to have not done this due diligence prior to bidding, the burden is now on you to discharge and clear all the pending dues affecting the flat 

this is the law

You are not liable to pay precise dues if they have not initiated any kind of action during last five years.

If they refuse to issue NOC you should approach civil court for suit of mandatory injunction against society for issuance of NOC.

If the bank has auctioned off the flat, they should have done it encumbrance free. Thus the flat previous arears maintenance fee should have been borne by the bank, not you. 

Once you have bought the property as is where is basis it becomes your liability to clear all the dues of the defaulter.

You can pay all the dues and gain entry into the flat after which you can take steps to recover the same from the previous owner by filing a money recovery suit against him for this.