Why don't we include internal motions of a body when finding kinetic energy? Say a person. There is a lot of stuff moving around. Yet when we calculate their kinetic energy we only look at motion of the whole person, not internal stuff. Why is that? Is it because that movement and velocities are internal to the person and don't add to the overall kinetic energy of the system?
Another example is a car. The Pistons and fuel and such are all moving around. However if we find kinetic energy of car we ignore that. I assume it because although the engine is moving, that energy is internal to the car only.
 A: These 'internal movements' of course contribute to the total kinetic energy. The point is, I believe, that in most calculations they are either irrelevant or negligible. When we address the question of "what is the kinetic energy of the person", we always address it in a specific context. Let's say we want to calculate this person's velocity when they jump off a trampoline. Then we assume that the internal movements are identical throughout this jump, and they represent degrees of freedom that do not contribute, affected or at all involved in the physical process that we are interested in. Therefore, we can just ignore them, which simplifies things greatly. Because if we want to invoke conservation of energy, for example, then $E_{\rm{internal}}$ before the jump and $E_{\rm{internal}}$ after and during the jump is the same, so it will not change our calculations.
Most of the times this is an approximation. For example a car in a collision will have its engine also affected. But we can assume that this change is small relative to the external kinetic energy that we consider, and that our results will be good enough if we assume that the kinetic energy from the movement of the internal parts of the engine is the same before, during and after the collision. The error will be very small (sometimes!) and the calculation immensely simpler.
This is not always the case. And sometimes these approximations fail. If we treat the car as a point-like object, we will fail to capture the full effect of the crumpling of the metal shielding, which is an important part of what makes modern car safer today since this crumpling absorbs a lot of the energy of the collision (instead of inflicting it on the entire car and the passengers). And I assume that engineers that build cars take this effect very seriously into their calculations.
It always depends on what we want to calculate and model.
A: If you think of it, the whole kinetic energy of the system is due to the internal energy, as in, the kinetic energy of every particle, being added up.
You may think of a moving ball. Think of how it gained so much of kinetic energy in the first place. Someone hit it. When they did so, they first transferred all their energy only to a single particle at the surface of the ball, and this atom transferred it's energy to it's neighbors and so on. 
So the amount of energy which was transferred to the first particle, is the same amount of the energy, all the particles have, if you add them up, which is indeed the kinetic energy of the ball (Neglect energy dissipations due to friction within the ball, etc)
In your case, if a piston moves, it does add to the kinetic energy of the car, but the energy is again distributed among all the atoms, but is very much present. However, you may not use it in your calculations, to not complicate things. 
And we usually don't look at internal stuff because, it's not necessary: since you're interested in the impact on the object as a whole.
You're just interested in 'what happens to the object A if it undergoes some change B' (as in, the course/book intends to teach only that) 
