I have finally got my corrected certificates, so I can enlighten the community a bit about the procedure.
The list of documents required for the correction are exactly as stated by the OP. My correction was approved after 21 days, and the school received my corrected certificates after just a week. The correction fees for each certificate is ₹ 750. The school will first create a correction request online on the Council website and upload soft copies of the original documents. You will then have to hand over your original certificates to the school and the school will send them to the Council. The Council will process the request after due verification, within a month. After the correction request is approved, the changes will automatically reflect in your DigiLocker version of documents, so keep checking (provided your year of passing ICSE is 2014 or later). The corrected marksheets will, however, come with ‘DUPLICATE’ inscribed on them, and you will not get pass certificates after correction, but instead, certifying statement of examination results.
There is no specific format for the affidavit and the newspaper notification. Make sure, however, that they clearly mention your name, year of passing, school name, and UID/ Index No. The newspaper can be either local or national, just that the matter must be in English. You can publish the ad in the local edition of the place you’re currently residing at or where your school is situated. Also, the affidavit should be by a First Class Magistrate, either executive or judicial, in English only, again executed at your current place of residence or where your school is.
I can assure you the Council cares for its students much, so it won’t take as much time for correction as for other school boards. I will say not to worry to anybody coming over here for help.
Please feel free to leave any other queries anybody has. I will try to answer as best I know from experience.