1) WRONG. Since gravitational force is an attractive force.
2) WRONG. The Earth does accelerate but the acceleration is so small that it's negligible. However it DOES ACCELERATE.
3) CORRECT.
4) WRONG. Mass means gravitational field, so Nina might be small compared to the Earth but it still creates a gravitational field around her. This answer is also wrong because it's breaking Newton's third law of action-reaction. If Earth pulls Nina, then Nina pulls the Earth back with the same force. Yes, with the SAME FORCE, however F=m*a, so the great difference in mass makes Nina's acceleration much bigger than the Earth's one.