Interpretation of rolling without slipping Here is an interpretation I came up with,
The friction, for a rolling body, converts the kinetic energy into rotational energy. Instead of dissipating it. 
Questions:
 1. Is my interpretation correct?


*what happens to the motion once all the k.e is converted to rotational energy?

 A: Rolling without slipping occurs when the static friction force between the rolling body and surface (e.g, tire and road) does not exceed the maximum possible static friction force of $f_{max}=u_{s}N$ where $N$ is the force normal (perpendicular) to the surface. For a level surface, $f_{max}=u_{s}mg$.
There is no dissipation in the case of static friction because there is no relative motion between the contacting surfaces. So static friction enables rotation without slipping. There is no conversion of kinetic energy to rotational energy. The rolling body has both translational kinetic energy (due to the translational motion of its center of mass) and rotational kinetic energy, due to its angular velocity and moment of inertia. If slippage occurs then some of the rotational kinetic energy is dissipated as heat.
There are two possible forms of heat dissipation. One is due to slipping and kinetic friction (due to relative motion between the surfaces). The other is rolling resistance. That's due to the inelastic compression and expansion of the material, such as the rubber of the tire, that occurs when the surfaces contact one another every revolution.
Hope this helps.
A: There is no such thing as "rotational energy". It is all just kinetic energy. However, it is often useful to break this kinetic energy up into two parts: 


*

*Kinetic energy due to the motion of the center of mass of the object (translational kinetic energy)

*Kinetic energy due to the rotation of parts of the object about the center of mass (rotational kinetic energy)


These are just useful "book keeping" labels; the difference between translational kinetic energy and rotational kinetic energy is not the same thing as the difference between kinetic energy and potential energy. It is technically still all just "kinetic energy".
Therefore, I would not say that static friction converts any energy, since static friction does no work here, and from what is discussed above there really is no conversion between different energy types. However, static friction is indeed a (sometimes the) force that causes changes in both rotational motion and translational motion (as compared to no friction being present). Something to keep in mind though is that you need some other force(s) present to cause static friction to be non-zero in the first place. For example, gravity with a ball rolling up a rough incline.

what happens to the motion once all the k.e is converted to rotational energy?

If this was the case then you would no longer have rolling without slipping, as the object would be spinning without translationally moving, which violates the rolling without slipping condition $v=\omega r$. This points to something to understand here: in rolling without slipping you can't independently "convert" between these two kinetic energies. If $v$ changes, then $\omega$ has to change in the same proportion. Therefore, friction can't "convert" one form to the other. Friction only allows these things to change in proportion to keep $v=\omega r$ valid.
