Why do rotating bodies have friction between when the surface is accelerating? For a body rolling with a constant velocity, there is no friction between the surface and lowermost point of the body, as there is no relative velocity between the body and the ground when it is rolling and no slipping. But if the body is accelerating with the help of another body or something, then the frictional force appears. Why is this happening? As here too, there is no relative motion between the surface and the lowermost point. I know that we need friction to create torque and so no slipping occurs. I want to know what is the difference between the two cases I mentioned. What is going on at the lowermost point of contact?
 A: You appear to be missing the concept of static friction and thinking only of kinetic friction.
Kinetic friction is the friction between two objects in relative motion, also called slipping. This friction force has a magnitude $F_{kinetic}=\mu_k N$ where $N$ is the magnitude of the normal force and $\mu_k$ is the coefficient of kinetic friction. The direction of this force is in the direction to oppose slipping.
The other type of friction is called static friction and it is a force that occurs between two objects that are not currently slipping. This force is interesting because it’s magnitude is an inequality $F_{static} \le \mu_s N$. Because it is an inequality it may take any value less than or equal to the maximum. Subject to that constraint, the static friction assumes whatever magnitude and direction is necessary to prevent slipping.
Note that usually $\mu_s \gt \mu_k$ so you can actually have larger friction forces without slipping than with slipping. This is the principle behind anti lock brakes on cars.
The friction force that you say “appears” is static friction, and it is whatever force is needed to prevent slipping.
A: Your statements do seem to apply to a rolling object.  If there is acceleration, the friction provides the torque required for the corresponding angular acceleration.
A: Possibly...
Static friction only acts when not only there is no relative motion between surfaces but also there is no met force acting on the body so in case of rolling with constant speed with no net external force, friction does act and in case of rolling with acceleration there is a net force so static friction acts.
Kinetic friction never acts in case of pure rolling as there is no relative slipping.
A: 
Static friction is a force that keeps an object at rest. It must be overcome to start moving the object. Once an object is in motion, it experiences kinetic friction. If a small amount of force is applied to an object, the static friction has an equal magnitude in the opposite direction.

In the case of rolling with constant speed, static friction is the friction that keeps the wheel rolling without slipping. The corresponding force on the contact point between the wheel and the surface on which the wheel rolls is directed backward, giving the wheel a forward motion. This force increases if the wheel accelerates (or changes from pointing backward to pointing forward when decelerating). If the acceleration reaches a certain value, the static friction changes into kinetic friction. The point of contact ain't stationary wrt the surface anymore and the wheel stars slipping. In that case, the force due to the kinetic friction gripping on the point of contact also points backward but this time, because of the energy released between the rotating wheel and the surface (think of the Formula 1 racing cars at the start: the cars are surrounded by smoke caused by this slipping) the kinetic friction is less efficient in accelerating the wheel (or decelerating it).
