Your Interrail pass is your ticket, so no, you don't need any extra tickets for a stopover.

You can’t add countries to a pass. You either have a one country pass, which is valid in one country only, or you have a global pass, which is valid in all countries. Travelling from Germany to Italy, a global pass seems most useful. You just need to register your journeys/train in the app (mobile pass) or in the travel diary (paper pass) and buy any mandatory reservations before boarding a train.

ONly possible with global pass. You just fill in the sectors by train you intend to make-and do that as late as possible-strikes, storms, changed plans, whatever can wreck all those plans you have thought about monthes advance. You do not even have to bother about what country the stop is in!

Thank you two very much! That perfectly helped me out :)