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Could we make a mode of transportation from one country to another through the interior of earth, by using the gravitational force as it would be faster and fuel efficient?
Answer 1:

No, for the reason of friction: not only is there rock and whatnot in the way, but any track that you would be running along will lose energy due to friction and turn it into heat, thus stranding you inside of the Earth. It's the same reason why if you have a U-shaped structure and you roll a ball down one side of the U, it will not make it as high on the other side. Friction scales with distance traveled, so most of your energy will be lost due to friction.

If there were no friction, it would take a trivial amount of fuel to travel across the Earth's surface - you would need the energy to accelerate to speed, and then the energy to decelerate to a stop. For a car, say, this would be the amount of fuel you would burn in about a minute of travel time (if that).



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