What is the nature of motion of an object falling freely under the action of gravity?

Show that the weight of an object on the moon is one-sixth of its weight on the earth. [Given: mass of earth $= 5.98 \times 10^{24} \ kg$,mass of moon $= 7.36 \times 10^{22} \ kg$,radius of earth $= 6.37 \times 10^{6} \ m$,radius of moon $= 1.74 \times 10^{6} \ m$]

$A$ stone is dropped from the edge of a roof.
$(a)$ How long does it take to fall $4.9 \, m$?
$(b)$ How fast does it move at the end of that fall?
$(c)$ How fast does it move at the end of $7.9 \, m$?
$(d)$ What is its acceleration after $1 \, s$ and after $2 \, s$?

Which is greater: the attraction of earth for $1 \,kg$ of lead or attraction of $1 \,kg$ of lead for earth?

It is found that the weight of an object is more at the poles than at the equator. So it is beneficial to purchase goods at the equator and sell them at the poles,provided:

The Earth is acted upon by the gravitation of the Sun,even though it does not fall into the Sun. Why?