How does friction act in rolling motion? In case of rolling, static friction at the lowermost point becomes zero once pure rolling starts. So how is that when we apply a constant force on the centre of mass of the spherical body (or any other body that roll) it will experience friction at the lowermost point even after it starts rolling?
 A: It sounds like you're more interested in the rolling resistance rather than the reaction to the force applied to the CG of the rolling body.
A perfect rolling object on a perfect plane will experience no rolling resistance. However, the real world isn't perfect. In particular, assuming that neither the object that is rolling nor the plane that is rolled upon is perfectly rigid, they both will experience deformation at the point of contact. If this deformation is perfectly elastic then there would be no rolling resistance, but for most materials this isn't true: the material has hysteresis, so that the restoration force is less than the deformation force.
This cycle dissipates energy, and this loss of energy is the rolling resistance. A steel cylinder on a steel plate will deform only slightly, and almost completely elastically, so there will be very little rolling resistance. But roll the same steel cylinder on a shag rug, and the rug will deform as the cylinder passes and not completely recover, causing a good deal of rolling resistance.
Hypermiling enthusiasts reduce their rolling resistance by using high tire pressures and narrow tires, sometimes even cutting away most of the tread to leave a single strip. All to increase the hardness of the tires and decrease hysteresis. 
A: 
In case of rolling, static friction at the lowermost point becomes zero once pure rolling starts.

That's not really true.
Consider the following digram for a monocycle.

Through the drive-train the rider provides a torque $FR$ to the wheel. If sufficient friction can be provided by the normal force $F_N$ and the friction coefficient $\mu$, the friction force $F_f$ will provide torque to make the wheel turn and pure rolling starts (if not the rider will 'burn rubber').
Now assume the rider has been pedalling for a bit and has reached a speed $v$. With pure rolling (no slippage) this also means:
$$v=\omega R,$$
where $\omega$ is the angular speed of the wheel. At this point say the rider stops pedalling altogther: no more forces act in the horizontal direction and no more torque is applied to the wheel. Newton then tells us the status of horizontal motion must now stay unchanged: $v$ and $\omega$ no longer change. That also means no more friction is needed. Imperfect tyres of course always create rolling resistance but that's different from what we're discussing here.
But as long as the rider wants to accelerate (or decelerate) friction is needed even with pure rolling.
