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.

I second the advices from @Mattheas  and if you consider to take Nighttrains i recommend to use the Paperpass as the through the Night the conductors change at every border and they control the tickets this means they would wake you up every time the train staff change.

With the paper pass you could give your ticket + reservation to the Steward and sleep the whole journey as the steward will show your ticket to the different conductors on the way. Usually the steward takes the whole journey with you :)

I don’t know where in Italy you’re from, but it may be possible to do your initial journey to Berlin by train in a day, or overnight if that’s something you’d be interested in.

For the daytime route from Rome, for instance, take an early-morning Frecce train to Bolzano, change onto a Eurocity to Munich, then an evening ICE to Berlin.

(Reservation fees in 2nd class are €24.50, or just €10 if you take a regional train from Bolzano to Brennero and catch the Eurocity from there)

Or for the overnight trip, take a train from wherever you are in Italy to Milan, then a Eurocity to Zurich, and board the Nightjet to Berlin.

(Reservation fees dependent on Nightjet accommodation choices. Once again, it’s possible to avoid the Eurocity reservation fee by catching it from the border; taking a Tilo regional train from Milan to Lugano and catching the Eurocity from there will save you €9)

I didn’t know that! Seems like quite a major mobile pass drawback, Interrail should advertise this properly or they’ll start getting complaints about it.

Maybe in future the first conductor to inspect the physical reservation-only ticket could stamp or punch it to confirm the traveller is in possession of a valid Interrail pass, before handing it over to the next one at the border.

Interesting thoughts, I didn't realise that! And you don't want to give your phone to the conductor of course.

Yeah the system is not perfect yet @EdM  nice suggestions :)
@Emma Broggini 
If the trip ends in Split maybe take even the Ferry to Ancona (Discount for Interrailers) and by train with your inbound journey from Ancona to your hometown.

Thank you so much @Mattheas @seewulf @EdM you all gave me amazing tips! 

I was wondering if you knew if I have to make a covid test for every state I shift from (one for Czech Republic, one for Poland etc...) -- I already read that I do not need one from Italy to Germany by train, but I can not find any information about theothers.  

The situation with test´s change weekly best is to use the websites of the Foreign and/or Tourist Ministery of the Countries visiting as they have the best and uptodate informations.

ReopenEurope is a good source for the start

Covid Informations by Interrail and Links to the local Ministeries

If you look at the Re-open EU website youncan see that a lot of areas are marked as green now. The ECDC has decided that when travelling between green areas there won't be any restrictions, like testing or quarantine requirements. I still want to be really sure though, because this would be that I could travel without restrictions this summer

The ECDC cannot decide such a thing because public health is a national (and sometimes regional) competency. It can only advise. Therefore always check the national requirements for entry.

I had been wondering about this myself. After your comment I asked ÖBB and they imply you won't be waken up for ticket checks. Do you have any other experiences or heard about it?

On the OBB Nightjets from Amsterdam/Brussels to Vienna/Innsbruck and Hamburg/Zürich - Berlin they didnt woke me up as this train is a full nightjet Service (even the ticket conductor is from Nightjet) on other Routes like Berlin - Vienna or Munich - Budapest they woke fellow travelers (i use a other special offer and doesnt have the problem by myself) 

It depends if the train is operated by one company them self or on several with Conductor changes at the borders