Conservation of Momentum v.s. Conservation of Energy

Hetware

That is not completely accurate. Most discussions of the subject include some reference to a container which exchanges energy with the molecules. Furthermore, if the molecules have any accessible degrees of freedom such as a diatomic molecule, the collisions are not necessarily elastic. At least from the view of center of mass.

That is to say, a collision can impart angular kinetic energy to the molecule which is lost to the translational kinetic energy. More complex molecules can have even more degrees of freedom. Some of these degrees of freedom "freeze out" at lower temperatures because of their quantum nature.

Two mono-atomic molecules colliding without exciting their electrons to higher energy states can be considered completely elastic.

rcgldr

The earth gains all of the momentum lost by the car, but since the earth is massive the change in earth's velocity (angular and linear) is tiny. The total momentum of what can be considered a closed system consisting of the earth and the car remains constant, ignoring any external forces (like gravity from the moon or sun).

As for the loss in kinetic energy with in-elastic collisions, in most situations, it's converted into heat during the deformation process. The relative amount of loss depends on how in-elastic the collision is.