Help understanding side-chain concept

I just finished IOHK’s whiteboard video about sidechains.

I felt like I absorbed much of the information like NiPoPow’s and the problems that sidechains can solve. However, I am left with a few burning questions:

1.) Do all sidechains require their own token, consensus, node operators, etc?
2.) How does the receiving chain mint the newly transferred coin? How is this even possible? I thought minting was only allowed based on a monetary policy. Is this a special exemption? I understand chain a will burn the token, and chain b will validate bc of the NiPoPow, but I don’t understand how chain b can mint a new token on request.