How does the fabric of space-time bends? So I get the analogy of the fabric of space-time bending as a sheet would bend with the weight of a ball on it, but that explains the "outside" how would the fabric warp inside the earth? Like the "line" passing through the center of the earth, would it be bent? What about some meters around it?
 A: The analogy of a sheet bending with a ball on it is just popsci physics.
In mainstream physics, spacetime is the collection of events that happen at certain places at certain times, but spacetime itself does not have a fabric that would stretch like a sheet (at least not like in that example with the ball).
In GR we use the expression, spacetime curvature, meaning the geometry is non-eucledian. 
To answer your question, yes, inside the earth, there is spacetime curvature just like outside it. The curvature depends on the stress-energy of the earth (not the mass contrary to popular belief), and the gravitational potential will determine the strength of the gravitational field. 
When you are outside the Earth, the closer to the center of mass (closer to the surface of Earth), the curvature will be stronger, but this does not mean that in your question, inside the earth, the gravitational field and the curvature will be stronger then outside the earth.
It is non-intuitive, but inside the Earth, the curvature can actually be less then on the surface of the Earth. It is because if you are actually inside the Earth, the matter (its stress energy) from all directions will affect you, and the net curvature might even be less then on the surface of Earth.

http://www.schoolphysics.co.uk/age16-19/Mechanics/Gravitation/text/Gravitational_intensity_variation/index.html
