No.

You can’t use it for any further travel in Germany, you will have to either pay separately for the German portion or travel via Italy.

AFIK the rule is that travel on any train that has a scheduled stop in your country of residence will trigger an In/Out day. If it simply passes through without a stop it shouldn’t trigger the use of a travel day. 

The app will prevent you adding any COR journeys after you have used both days. If you haven’t used both days it will flag that the journey requires an In/Out day and you need to confirm it.

If it's for the night train from Paris, then there's a specific fare for when your pass doesn't cover all countries involved, although a Sparschiene may be cheaper.

I believe that to be incorrect - Unless the train has no scheduled stops in your home country any journey through you country of residence will take an In/Out day or not allow you to add your journey if you have used all available In/Out days  - Even if you do not leave the train.

Otherwise pass holders could put their departure and arrival in the two countries (e.g. An Austrian on the ECB trains would put Verona and Munich)  and then leave at an Austrian station nearest home.