Deriving log-linearized equilibrium in Galí (2019)

I am reading the Paper "The effects of a money-financed fiscal stimulus" by Galí (2019).

I am trying to derive the log-linearized equilibrium as given in equations (15)-(22). I believe I am able to derive all equations expect for equations (17) and (20). I suspect that equations (12) and/or (13) should be used in deriving at least one of (17) and (20) (and possibly both).

Does anyone have any idea how to proceed?