1) When the Germanic tribes in Bohemia, modern Eastern Germany, and Poland were supplanted and assimilated by the Slavic tribes moving west?
Ethnic identity is really changing and proteiform without a political structure able to define a stable one. Generally, a tribe wasn't 100% "Germanic" or "Slavic" in most of the Barbaricum (these concepts being, ethnically, void) but rather a mix of whatever you could find, fitting in the shoes of tribal structures.
While the Vistula region clearly knew a demographical decline by the IInd/IIIrd (mostly due to epidemics and climatic changes, probably more than migrations), it remained as much clearly inhabited by the rough same populations : it was a smooth progress that probably looked like the "germanisation" of Germania in the IInd century BCE that ended up with a mix of Celtized and Germanized features.
It was probably helped by the appearance of the Avar Khaganate, whom peripherical peoples were structured along a slavicized elite coming from beyond the Vistula, and having a definitively less "German" overlook (but probably more sarmatian IMO). As the formative states around the Avar hegemony (in the same way you did end up having formative state arounds Roman or Carolingian hegemony) went trough an ethnogenesis dominated by slavic identity (rather than ethnicity in the strictest sense), you ended up with a clear slavification process that couldn't be recorded so far.
While it's hard to pinpoint a departure point that probably didn't have existed as such in first place, it was probably a thing in the VIth century already.
2) Who lived in present day Hungary, Romania, and Bulgaria before the Slavic migrations?
Your usual mix of Romans and romanized Germans or Sarmatians south of Danube, in different proportions but in relatively few numbers (Illyricum suffered a lot from Late Antiquity epidemics, climatic change, raids and economical decline). North of Danube, more or less like in the Vth : more or less romanized Germans and Sarmatians, possibly some scattered remnants of the Hunnic confederacy.
Did Slavs settle in present day Romania at all?
Slavs basically settled everywhere in Balkans up to the Mediterranean Sea. In some places they get assimilated, in some places they did assimilated. It depends a lot of the regions, even outside Byzantium.
3) Were there any Iranic speaking peoples left on the Ponto-Caspain steppe at all by this time?
Alans were, altough they were probably part of various tribal confederacies, that they don't seem to have been leading : Avar, Bulgars, Khazars, etc. and their own direct presence was eventually limited to Caucasus piemont, in
Alania.