None of this is completely correct. You’ll need a supplement for the Innsbruck departure and a reservation for the Verona departure.  

At least if you’d like to use the EC trains.

Thanks. Sorry the departure time is actually 8:28 out of Hallstatt. Never paid a supplement when I have used the Rail pass in the past.  Please explain. The trains in question are the EC 85 out of Innsbruck 13:24 and the EC 44 out of Verona 16:58. But again DB and Thomas Cook list no reservation needed. I’m puzzled. I have traveled this same route many times in the past without a seat reservation, but I have never used this Rail Planner app, so i do not know what their street cred is. Again thanks

Yes, I thought you'd like to take these two trains. It also has nothing to do with the app; it does just tell you. It would be the same with a paper pass. 

You need an "Aufpreis Brennerverkehr Passzuschlag 1" for  the Innsbruck departure. It will cost you 10 € 2nd class or 15 € 1st class. 

DB and TC are both right: You don't need a reservation. But you need this supplement. 

Long distance trains in Italy (all Frecce and EC) need a reservation for passholders that will cost you 10 € per train.

You can go by regional trains without any additional costs. 

Yes, as progress comes=much more wide used and cheap IT and as more+more of those new fancy hi-speed lines are opening and more and more railways are going airline style on providing all pax with a seat-REServ these supplmts are now getting more and more wide. It is by now IMPossible to use overnite trains without them (except the few seats-only ICE remaining in Germany).

OTOH the ease in getting these REServ-when needed-is also dramatically higher as it used to be before.

A few years ago the whole pass-system was on the brink of collapse as indeed those railways with loads of hi-speed that they need to make money on started/were allowed to charge rather high SURcharges to use these trains- the result is now that about each&every newbee here seems to exactly want to ride those sectors and all come with exactly the very same problems etc.