To book reservations you can book also via Interrail.eu website (wich is also on the app), but I don’t recommend to book there, often it doesn’t work and it cost more than to book directly at the train company.
For Italy and France you can book directly via ticket office of SBB CFF FFS. Online possible for Italy via tickets.oebb.at using ONE WAY TICKET option and adding as discount at adult “Interrail/Eurail Global Pass”.
For Germany, Austria or Czech Republic book directly via DB, ÖBB or CD with the seat only option.
Here a tutorial for reservations: How to get Reservations :) | Community
P.S. You can add your Paper Pass in the app and add the trips there, or use it the old way with writing every train on the pass with pen. Record your journeys in the app | Interrail.eu