The procedure followed by the society in transferring the flat to the sole name of the wife is incorrect
Ideally the society ought to have insisted for a letters of administration or an heirship certificate
Mere giving of an affidavit with some indemnity and public notice is not sufficient
You can buy the property now but in the future if you go to sell it and the buyer is funded by the bank then you will face problems to get a suitable buyer in absence of a valid LA or heirship certificate having been granted to the lady who claims that she is the sole legal heir of the husband
The lady's title is clear only in respect of the her 50% undivided share and as regards the balance 50% which she inherited from her husband, her title is defective as there is no registered transfer deed in her name which can be made only after a LA is obtained from the Court
Obtaining LA or heirship certificate is a lengthy procedure and is also expensive as it involves payment of court fees with professional fees of the lawyer and clerkage and other miscellaneous expenses. It takes about 8 to 10 months to get the LA provided there is no challenge raised against the grant of LA
Once the LA grant is obtained, the administrator appointed by the Court will have to register the transfer deed in favour of the lady. Since its transfer of 50% share to the legal heir, there will not be any stamp duty as applicable on a sale deed. Registration fee will be extra.
As regards other NOC etc., it's just the share transfer forms and a limited POA from the lady to enable you to apply to the various authorities for effecting mutation in your favour in their records. The POA can be used to sign on any application on behalf of the seller.