For example, when we put two objects of +10C and +20C together and then take them apart, each of them acquires a charge of +15C.
This is not always true. It is true only if the objects are conductors. If the objects are not conductors then they will each retain their original charge when separated.
Why is it that then neutrons has no charge and why does 1/2 the charge of proton not be transferred to neutron?
The nucleus is not a conductor.