You are misunderstanding the difference.
Potential energy is just that...potential. If a rock is sitting on the side of a cliff, it has potential energy. Another way to think of it is as
stored energy. A rock can sit on top of that cliff for a thousand years and the energy is just stored. A cyclist standing at the top of a hill also has potential energy but as with the rock it is only "potential" energy. No movement has occurred.
Kinetic energy is what results when the rock falls or the cyclist starts down the hill. That energy that the object "potentially" had at the top of the hill or cliff is converted to movement.
Kinetic energy doesn't need to be considered. If we start at the top of the hill from a stand still, then there is zero kinetic energy. If we are already moving when we reach the descent, then there is a small amount of kinetic energy, but this is negligible compared to the energy embodied in the height change. Furthermore, assuming you continue rolling after reaching the bottom of the hill, whatever kinetic energy you had at the start of the descent is carried over to the end of the descent, and can be completely ignored from the heat calculations.
Kinetic energy is that
only energy that
can be considered. Once you start to move, the energy is equal to 1/2mv^2 where m is the mass of the object and v is the speed of the object. If the object isn't moving, it's energy is zero. It has the
potential to become energy but not until it moves.
Any energy you have left over at the bottom of the hill still gets converted to heat when you eventually stop the bike. It may not be important for heat build up on the braking system when braking on a hill but it is still there.
If you simply insist on thinking of kinetic energy, you can consider the potential energy as being converted into kinetic energy during the descent, and then subsequently converted into heat. This is more intuitive but the two step calculation is mathematically unnecessary.
Exactly. And that's the only way you can consider it. Potential energy is based upon the work needed to lift an object to the top of that hill. You use kinetic energy to lift the object...either quickly in the case of the bicyclist or slowly in the case of the rock at the top of a hill. But the energy is converted to kinetic energy once the object start to move. That's what "kinetic" means "of, relating to, or resulting from motion." The equation for kinetic energy above only works if the object is moving.
So, following from the above: the rider's potential/kinetic energy is converted into heat via friction (air and pads) and compression (air). The heat then dissipates into the atmosphere. I'm not sure what you mean when you say "the heat goes into the atmosphere not due to air resistance but due to radiation". This is a non sequitur. Air resistance is what creates the heat in the first place. Once heat is created, it can then dissipate. The majority of the heat transfer occurs via convection, not radiation. Radiation only overtakes convection when the surrounding pressure approaches a vacuum (i.e. cycling in space).
Not a non sequitur at all. Even without any wind, the heat will dissipate through radiation to the air. The air then can move due to differences in density of the air.
Air resistance only creates a tiny amount of friction and thus heat. This has little to no effect on the friction of the brake pads on the wheel. It is the friction of the pads on the braking surface that creates the heat of braking. Air sweeps the heat away but only after the surface radiates the heat to the atmosphere.