What Tosafos says was used by the debates many times, to show that the Gemara doesn’t make fun of, or even discuss, Oso Ha’ish. Some say that Tosafos didn’t really mean it, either. The Seder Hakabala of the Ra’avad mentions the two views and says that he thinks it was one. The Ramban in his debate said that we beleive he was earlier and they say he was later (in order to claim the Churban a retribution for not accepting him).
The Minhag was known in the Litta, but was dropped in the Yeshivos. By now, it is not their Minhag anymore.
The word, Nittel, comes from Nettle (or something like that), which means birth. That was the name the gentiles called it. Perhaps we changed it a bit to Nittel to mean, taken, as opposed to, birth.