Right now, at this moment, the Earth is exerting a gravitational force on you. Are you are aware that you are also exerting a gravitational force on the Earth? Look at the formula GM1M2/r2 is . Newton’s 3rd Law is embedded in Newton’s Law of Gravitation!
In the region between the Earth and the Moon, an object would be pulled by the Earth and the Moon in opposite directions. The gravitational null point is the position where an object experiences zero net force. Do you know how to calculate that position?