Does gravity have any effect on inertial mass?

$(i)$ Is the acceleration due to gravity of earth '$g$' always a constant at every place? Discuss.
$(ii)$ During a free fall,will heavier objects accelerate more than lighter ones? Give reason for your answer.

On what factors does the value of acceleration due to gravity depend?

The value of $g$ on the earth's surface is $9.8 \, m s^{-2}$. Suppose the earth suddenly shrinks to one-third of its present size without losing any mass. What is the value of $g$ on the surface of the shrunk earth (in $, m s^{-2}$)?

When dropped from the same height,a body reaches the ground quicker at the poles than at the equator. Why?

The atmosphere is held to the earth by