I will try to have a look at this, but this might take some time.
1.) You are confusing quarterly and annual inflation. See e.g. the section on inflation in Pfeifer (2013): "A Guide to Specifying Observation Equations for the Estimation of DSGE Models"
https://sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf.