Huh, Orthodoxy is very old and widespread. Ofc during Communism, it tended to be suppressed, but as a bedrock of the society, Orthodoxy definitely prevails in Serbia, Rumania, Bulgaria, Macedonia, Belarus and Russia at least.
Ukraine is more complicated, a nation sewn together from very different regions; Greek Catholics are an important minority, mostly present in the formerly Austro-Hungarian western part of the country, which also seems to be the most nationalist one.
Presumably these studies have been done recently, not two centuries ago, so I'm not sure how useful they are in determining that Orthodox states are "more corrupt."
I am not sure either, but I wouldn't rule it out either. Caesaropapism was probably, on the net, a negative shaping force in societies which indulged in it.
In the world of Islam, the Shi'a system of ayatollahs is structurally fairly close to Christian Orthodox Churches, and the Iranian theocracy which builds on it is corrupt beyond belief.
That said, it probably makes sense to study why some countries are somewhat less corrupt or how they managed to keep corruption in check. Corruption seems to be fairly widespread across space and time, one of the universal blights of mankind.
Ukraine is more complicated, a nation sewn together from very different regions; Greek Catholics are an important minority, mostly present in the formerly Austro-Hungarian western part of the country, which also seems to be the most nationalist one.