IB Physics Gravitational field strength

A tutorial sheet of questions on gravitational field strength is below.

1. The mass of the Moon is 1/81.3 that of the Earth. Assuming a model in which the bodies are considered to be point particles at rest, find the location of the point in space where the resultant gravitational field is zero.
2. In question 1 consider of model in which the Moon moves in a circular path about the centre of the Earth. Does the zero field point move closer, stay the same or move further away from the Earth? Calculate its position assuming an orbital period of 27.32 days.
3. In question 1 is/are there points inside the Earth or the Moon where the resultant gravitational field strength is zero?