If the Babylonians castrated all the exiled Jews, there would be few Jews to return to Jerusalem after a period of around 60 years. While the Jews were certainly exiled, most of them were not kept in slavery. The main reason to castrate would be to keep slaves in harems, and Jewish tradition does not really discuss whether Jews were employed in Babylonian harems. There are biblical suggestions that eunuchs may also have been employed in Judah during the late monarchy, but the wording is ambiguous and can not be relied on in that sense.
That is not stated explicitly, since even the relevant Hebrew word (sris) doesn't always mean castration. The answer is that it is not unlikely, but probably only in some cases, not all.
Egyptians
It was destroyed by the Babylonians in 586 BCE
The Hebrews, Bnai Yisrael, Children of Israel, Hebrew Slaves, were the Slaves of the Egyptians.
The tribes were kidnapped and taken into Babylonia by the Babylonians.
Yes, Giuseppe Verdi wrote Nabucco, Chorus of Hebrew Slaves.
No. Ancient Hebrew is a language, not a place.
contests between wild beasts, i.e. lions and human slaves
The Jewish answer is that the Babylonians did not change the Jewish faith. Our traditions, which we still keep, have been around since long before the Babylonian exile.
yes they did.
the deliver of Hebrew slaves
Moses discovered his Hebrew heritage and realized he was not an Egyptian when he saw an Egyptian taskmaster mistreating a Hebrew slave, prompting him to intervene and ultimately leading to him fleeing Egypt.
Hebrews have been slaves (or second class citizens at best) to the following: •The Ancient Egyptians •The Babylonians •The Persians •The Assyrian Greeks •The Romans •The Muslims •The Catholic Church •The Russians •The Nazis