Yes, the work done by the net force acting on a particle depends on the inertial reference frame of the observer.
Yes, the change in kinetic energy so depend.
Newton’s laws are valid only in inertial frames of reference. If we find Newton’s second law to hold in one frame of reference, then it holds in all inertial frames. If two observers in different inertial frames move at constant velocity v relative to one another and observe the same experiment, they measure identical values for the forces, masses, and accelerations, and so they agree completely in their analysis using Newton’s second law.
In the Newton’s second law, observers in different inertial frames will agree on the results of applying the work energy theorem. However, unlike forces and accelerations, displacements and velocities measured by observers in different inertial frames will in general be different, and so they will deduce different values for the work and kinetic energies in the experiment. Therefore both the value of work and kinetic energy depend on the reference frame of the observer.
Let us consider an observer is at Mars observes the movement of two object which is present at Earth’s surface. Both the observers observe to each other at rest in the Earth’s surface. But according to the observer which is at Mars observes both the objects are moving. Therefore the value of kinetic energy depends on the reference frame of the observer. Again since the net work done by the forces acting on a body is equal to the change in the kinetic energy of the body, thus the value of work depend on the reference frame of the observer.