Some help with this would be appreciated.
I just have one answer : You take into account the real wage cause you want to simplify the model. If you put the inflation then the model will have the Cost Inversion ( which have the inflation).
Nominal output is simply P*Y. Usually, with the Solow model you are interested in real quantities, i.e. the number of goods produced. The intensive form of the production function is obtained by divided through by labor, you would get y = f(k), where y = Y/L and k = K/L.