Paris and Eastern Europe is 31 Days.

Berlin, Prague, Vienna at least 3 days each, Salzburg, Munich, Dresden 2 days. Altogether with your other destinations if I counted correctly equals 31 days. I guess you have a reason to stay in Dusseldorf 4 to 5 days?

6/2 fly to Paris - 3 nights
6/5 fly to Warsaw - 2 nights
6/7 fly to Budapest - 3 nights
6/10 train to Vienna - 3 nights
6/13 train to Salzburg - 2 nights
6/15 train to Munich - 3 nights
6/18 train to Prague - 3 nights
6/21 train to Dresden - 2 nights
6/23 train to Berlin - 4 nights
6/27 train to Dusseldorf - 4 nights
7/1 fly back home

I think David's itinerary shows that you are trying to see too many places in the time you have. Most of your journeys will use up 1/2 day. You'll need time to pack/unpack, check in/out of hotels, get to/from train stations or airports (far from city centers), and if you are flying, lots of extra time for checking in, checking luggage (low limits on those short flights), security checks, boarding time, baggage claim time. You'll have little more than:
Paris - 2 days (at least one with jetlag)
Warsaw - 1 day
Budapest - 2 days
Vienna - 2 days

Well, you get the idea. And check the bahn.de website for train schedules. I just looked at Munich-Prague, and the journey time is nearly 6 hours. If you want a whirlwind trip, maybe that plan works for you. I wouldn't like spending so much of my time traveling from place to place and having so little time to sightsee once I'm there.

Dropping Warsaw would slow things down a little.
You would have 2 nights to allocate elsewhere, perhaps to Vienna and Budapest, and also leaves one less flight to worry about.

Salzburg/Munich are also outliers if you visit Prague.

Why don't you pick three or four cities, maybe Paris, Budapest, Prague, Warsaw (if that interests you) then rent an apartment in each, spend 6 to 8 nights in each and do day trips and an occasional over night trip. Less packing and unpacking that way. more time to just enjoy.