How does acceleration due to gravity depend on the mass of the planet?

An object is placed one by one in three liquids having different densities. The object floats with $\frac{1}{9}$, $\frac{2}{11}$, and $\frac{3}{7}$ parts of its volume outside the liquid surface in liquids of densities $d_1$, $d_2$, and $d_3$ respectively. Which of the following statements is correct?

It is said that the mass of an object remains constant at all places,while its weight may change. Why?

What is meant by acceleration due to gravity? Suppose a planet exists whose mass and radius both are half of that of Earth. Calculate the acceleration due to gravity on the surface of this planet.

$A$ man at the top of a tower throws an object horizontally,whereas he simply drops another. Will these two objects reach the earth at the same time?

State the universal law of gravitation. Write the $SI$ unit of $G$.