Question about Gili (2008) chapter2.mod

Dear Prof. Johann,
I am a new PhD student in Economics. I read the model Chapter2.mod from JohannesPfeifer/DSGE_mod (Github) but I do not know how to get the following derivation from equation 22? Why Pi(+1) disappears? Could you explain a little?

//6. Monetary Policy Rule, eq. (22)

And one more question: in Chapter 2.mode, why monetary policy shock lead to a decrease in Pi? I cannot see the Economics intuition. Looking forward to hearing from you.

Oh, I understand the first point. Hope you can explain second question a little bit.

What do you mean? An increase in the monetary policy rate should decrease inflation.