If kinetic energy increases, does the potential energy increase as well?
No. Kinetic and potential energy are inversely related, if one goes up, the other goes down. Think of potential energy as the energy that has been bottled up inside something (like the water that is in a bottle) and the kinetic energy, as the energy that has been (or is being) released (like the water that has been poured into a glass and therefore it is not in the bottle anymore). The potential energy is the amount of energy that something has stored inside it while kinetic energy, is the energy that has been released. So if one goes up, the other goes down.
