Trains in Eastern Europe

I can't answer the flexipass part of your question and I'm no expert on the rest, but I am making plans myself for much of the same itinerary, also in April. I'm using a combination of Thomas Cook's European Timetable, since I'm a luddite and I still like to sit in my recliner and READ a book, plus www.bahn.de, an excellent online website covering nearly every part of Europe. I'd say yes there are daily trains but I'm not sure about whether there's a train, say, FROM Varna TO Brasov directly, or other combos of the cities you listed. Hit me back if you think we might cross paths, esp in Brasov, where I intend to park for a night and day to see Peles and Pelisor about mid-April! Happy training.

In general, from past experience and research, train passes are not normally a good value in this part of the world because: a) point to point tickets are reasonable and quite often cheap
b) trains lines/routes are not as extensive as other parts of Europe - on a number of routes, buses are more direct, shorter in duration, and cheaper You can always look at the deutche bahn website for all the trains to see what the possibilities are.

Train travel in that part of Europe is more difficult than in western Europe. We went from Istanbul to Stara Zagora, Bulgaria. That was a fifteen and a half hour trip over night in a horrible six person couchette. The car looked like it was fifty years old. Then we moved from Stara Zagora to Bucuresti, another long, hard overnight trip in an old car. From Bucuresti we went through Brasov, only this time we bought a first class overnight ticket and so had a two person couchette which was very nice, but we had to get up in the middle of the night for a border crossing. Train travel is cheap, but you really have to love it to make it work. From Bucuresti we took a bus out to Constanza, and back after a few days. That ride was a pleasure. Whatever you do don't travel second or third class unless you want squat toilets and memories to last forever.