If only vertical load applied on a single pile, which the pile has the soil reaction modeled as a spring, Does the pile axial force will be changed if the spring stiffness changes?
Axial force distribution will depend on axial stiffness. If all piles have the same axial stiffness, then the load distribution will not change. But if you have piles with different axial stiffness, then the load distribution will be different.
The other important thing that will need to be accounted for the is the rigidity of the pile cap, whether it is rigid or flexible.