I will try to make a very approximate answer for your mother (as requested), assuming
the Earth spherical, and several other approximations. I am no expert
in geophysics, or stellar physics. and if you want details or greater
accuracy, I suggest you look at other answers, such as that of David
Hammen and others.
First regarding gravity. Is there gravity at the center of the Earth,
and if not, why should anything be attracted there?
A basic exercise when studying gravity is to
compute the force gravity inside an empty spherical shell of matter
(like the rubber of a basket ball). The answer is: there is no gravity
produced by the spherical shell inside the shell , though there is
gravity outside produced by the shell.
If you now consider a shere filled with matter, will a 6371 km radius
(like the earth), and a point at 5000 km from the center, you can
decompose it into a full sphere of 5000 km radius and a spherical
shell around it with 1371 km thickness. The spherical shell causes no
gravity, hence, all the gravity there is to be observed is that
produced by the sphere of 5000 km radius.
This is actually true for any radius, so that, at the center of Earth,
i.e. with a radius 0 km, there is nothing left to produce gravity
since all the matter is in the "shell".
But that does not matter too much since, there is some gravity towards
the center as soon as you get at some distance from the center,
however weak when close to the center, so that with time, havier
matter will tend to sink to the bottom, i.e. to the center.
Then there is the issue of what is heavier.
What is Earth made off
Original matter in the universe (not going back to the Big Bang
though) is composed of mostly very light element, mostly hydrogene.
Stars form by accretion of this matter under gravitational forces, and
start fusing it (nuclear reaction) into heavier elements, and produce
energy we perceive (partly) as light. They tend to produce a lot of
elements like iron (and others that around the "middle" of the table
of elements, becauses these have the most stable atomic nucleus from
which little energy can be extracted, so that stars die (in various
ways) when they have transformed their matter into such
elements. Final explosion of some stars (supernovae) produce heavier
elements, but not in such great quantity. This (very grossly) explains
why iron (and some other elements) tend to be available in greater
Why is matter not stratified by density.
Again I am no expert, by there is a variety of phenomena that are at
work. Here are two examples.
Indeed, since at least part of the planet is somewhat fluid, one could
expect that te heavy components would sink. But there is much heat
produced inside the planet, due inparticular to radioactivity, and
this heat produces convection (and thus continental drift). Convection
means motion, moving matter around. That is more a dynamic aspect.
Another phenomenon is that chemical elements are seldom pure. They
combine physically or chemically to make composites that have
different physical properties. A compound formed of a heavy element
and a light one can be fairly light and float the heavy component
towards the surface of the planet, the lighter part playing the role
of a buoy. So, though uranium is much heavier than iron, uranium
composites with lighter elements can be found on the surface of the
planet, or very close to it. The phenomenon depends much on the
ability of the different kinds heavier elements to combine with
You must also take into account that Earth took a long time to form and importance of different phenomena may have changed over the course of its formation.