What is the magnitude and direction of the gravitational force that acts on a woman who weighs 500 N at the surface of the earth?

The force acting on the woman is equal to 500 N as stated in the question!.

Remember: Force (N) = Mass (kg) x Acceleration (ms-2).

As such to create that force an acceleration must act on a mass. The gravitational acceleration at Earth's surface is equal to approximately 9.82 ms-2.

As such a woman who weighs 500 N would have a mass of approx 50.9 kg.