Answer your queries on a depository's activities, as well as CDSL, in this glossary of Frequently Asked Questions.
a) No, the Issuer / RTA issues new certificate/s with generally different distinctive numbers.
b) The new certificate/s may be issued under new folio number or in the existing folio, if investor already has one with the company.
The Issuer or RTA, as the case may be.
No. Remat does not amount to a transfer and does not attract any stamp duty.
A beneficial owner can remat his holding even if it is an odd lot.