In any case, if the force and power is constant , does velocity also need to be constant? If no, can you tell me a case. Further can this be extended for non-rigid bodies.
If the velocity is constant, there is no acceleration so there is no net force.
So, consider an example where an external force acts on an object that also experiences an oppositely directed frictional force proportional to the speed of the object.
There will be a speed where the two forces cancel and the object will no longer accelerate.
The power delivered by the external force is then constant but rather than increasing the KE of the object, the energy is converted into heat and the power is the rate of that conversion.