Stationary and Non-stationary variables in panel

[popcorn]

I am a bit confused when it comes to regressing I(0) and I(1) variables in panel. Normally, variables are I(1) and then one simply differences them in the regression. However, what happens if I am estimating either a Pooled, Random or Fixed Effects model and I have the following variables:
Dependent Y (which is I(0))
and the explanatory variables are:
X1 (which is I(1)); X2 (which is I(0)); X3 (which is I(1)); X4 (which is I(0))
I also have a dummy called DUM
Do I difference all the variables - even the I(0) variables?
Or do I estimate the pooled, FEM or REM models as : Y= dX1 + X2 +dX3 +X4 +DUM
or dY= dX1 + dX2 +dX3 +dX4 +DUM

Am I correct that I do not difference the dummy?

Thanks for your assistance and response.