A. Buying an immovable property through a power of attorney deed is invalid and illegal. There is a supreme court ruling itself for this.
You can enter into a registered sale agreement on yur name which will be a valid and proper procedure.
B By power of attorney deed there is no conferment of ownership of property.
POA deed is not a title document. It is just a licence to represent on behalf of the owner.
C Yes. After the death of the principal, the POA deed becomes revoked or infructuous automatically.
D. You can sell the property only during the effective period of the POA and not after the death of the principal who executed the POA in your favor.