What are the relationships between gravitational potential energy vs. position, kinetic energy vs. position, and total mechanical energy vs. position?
The gravitational potential energy of an object is dependent on the distance of the object from the center of the Earth which, as we measure it, is the height of the object. If the position of an object is higher its gravitational potential energy is also greater.
The position of an object does not affect its kinetic energy. Kinetic energy is a product of the mass of the object and the square of its velocity. None of these are dependent on its position.
For an isolated system, the total mechanical energy in the system is not affected by the position of the system. If the system's gravitational potential energy were increased by making it move to a higher position that would decrease its kinetic energy and if the kinetic energy were increased by allowing the system to fall to a lower height it would lead to a reduction in its potential energy.