What is the value of $g$ at the centre of the Earth? Is it zero or infinity? My attempt: I know it's zero but applying law made me on fused.
According to the shell theorem, there's no gravitational attraction inside a spherical shell of matter. At the center of the earth, its entire mass is arranged around you in spherical shells, so the gravitational acceleration due to the earth is zero.
You'd still feel the gravity of the sun and moon and other external objects, as well as a (small) contribution from the fact that the earth isn't quite spherical.
I'm not a physics expert, but I do know the basics. Gravity is created by mass so all things with mass have gravity. The gravity is negligible in an object unless it is something large like the earth or moon. In the middle of earth, all of the mass should be all around you so you should feel the force of gravity pulling in all directions away from you.