Sounds like a great and diverse itinerary! Sarajevo is a bit of a hard place to reach, because there are no international railway connections anymore. I would advice to get to Sarajavo from Split by bus (not included). It's also possible to then take the train to Mostar (another pretty city) and then back to Split by bus. Sarajevo-Mostar is a scenic ride. Or choose a different city altogether, like Ljubljana or Bratislava (if you wanna break up your journey earlier along the way). It's up to you!
5 travel days sounds like a great choice! To save yourself some time and a ho(s)tel reservation, you could extensively use night trains on your journey. Warsaw - Prague, Prague - Budapest, Budapest - Split all have night trains connecting them. You could also do Prague after Berlin, which lets you travel along the scenic Elbe Valley. Then night train to Warsaw, then night train to Budapest.
For your pass, in case of a mobile pass you can load it onto your phone on the Eurail Rail Planner app. You can activate it as late as on your travel day this way! You then need to connect a trip to your pass in the app. Some trains do require reservations in advance, like night trains or some other long distance trains. I'd try making these at your local train station with a ticket office. Otherwise I also have great experiences with Deutsche Bahn, ÖBB or SBB call centres. If you feel comfortable calling in English of course! This way reservations are sent to you by mail for a small extra fee. You can always book while travelling, but that leaves the chance that your train is fully booked or there are no Interrail seats available anymore.
Hope this helps! Lemme know if you wanna know more.
