What should we do with the body of an unidentified woman found on the seashore? Should we bury her assuming she is Muslim, or leave her for the Hindu government to deal with according to their beliefs?

It is not permissible for a Muslim to bury a non-believer, except out of necessity, on condition that the burial does not face the Qiblah and is performed without observing the Sunnah. If the religion of the deceased is unknown and there are no indicators, they are treated according to the majority religion of the inhabitants of the place where the body was found.