Can someone be allowed to operate my demat account on my behalf with the powe of attorney?

Yes. Yes. You can authorize anyone to manage your account by signing a power-of-attorney. You will need to send a Notarized copy of the POA along with your DP. Make sure that both the Donor (or Donee) sign the POA. KYC rules apply to the POA holder. If the POA is submitted at account opening, the bank will require that the POA holder sign the account opening document.