1. Newton's third law can relate to running since as one runs, they exert enery on the sole of their foot, on the ground and in return, the ground pushes back an equal and oppositer force. This demonstrates the action-reaction theory. Moreover, in Newton's second law, it states that acceleration is produced when a force acts on a mass. If one starts at rest, and begins to move there is a force involved in this movement. In running, it is evident that by putting a force on the sole of the foot and pushing down on the ground (mass), acceleration is created by gaining speed.
Kinematics can be associated with running because we know that it is a form of motion. To run and attain our desired velocity (v2), we normally start at rest, or a slower speed (v1), and in order to achieve a faster speed in a certain amount of time (trying to outrun another person) there needs to be acceleration. This can be shown using the formula:
a = v2 - v1/ t and by d-t, v-t and a-t graphs.
Description of motion: A runner starts at rest, then gains speed and reaches a constant speed.
2. Running shoes are designed to optimize performance by creating a light and flexible shoe. This is beneficial during performance because if the shoe is lighter it will allow the runner to use less energy in lifting the shoe and compressing it, thus using the energy to win the race! The most efficient shoe will be as light as possible, not compress at all, and will not slip on the ground.  In order to achieve this long distance, running shoes typically need to protect runners from impact in order to prevent damaging joints, which isn't a good thing! The shoe will most likely have a soft midsole and both the heel and forefoot areas will be more resistant to compression. 
Furthermore, the heel and forefoot areas have higher impact, therefore are made to absorb more shock.  These areas also need to be resistant to compression because if they aren't this will cause the runners to waste much energy in compressing the sole rather than using the energy in motion.
In regards to grip and friction, the bottom of a running shoe should be flat for a track surface in order to prevent the shoe from slipping. A flat shoe is beneficial for the track because it provides a full surface area contact and will not have additional weight/material on the outsole. 
3. I don't believe that improvement in equipment necessarily makes better athletes; however, it can improve their peformance. Factors contributing to good athletes can be physical, mental and emotional well-being. Although better equipment can enhance peformance making them more recognized athletes in general. For example, lighter shoes makes it easier for an athlete to run faster since they don't have to carry extra weight with them during their run, thus using up more energy. Also, the use of specific materials can cause more or less friction on the ground depending on the material, which affects performance. As mentioned in part two, the shape and design of the shoe can impact the athlete's performance because it can affect the amount of impact one gets. Moreover, friction is affected by the shape of a shoe (for example, flat); since it gives a larger surface area to push off of.
Therefore, improvement in sporting equipment does affect athlete's performances, but in my opinion it doesn't certainlly make “better” athletes.