Migration happened on the same sim. So, I didn't have to pay any fee. Btw, it was a regular sim replacement which I did (they didn't told me to take new sim). They took Rs. 25 for sim replacement.
Yes, it is working.
You'll have to do FRC from airtel store. They'll tell you the pack and price. I did a recharge of Rs. 495 (FRC) which gives me 1.4 GB per day for 84 days.
Nothing, they didn't ask me for any document. But you'll need to take your airtel number with you for OTP. For sim replacement they asked for original document of photo and address proof.