I will try to answer the first question on whether Hallel was recited on Yom Nicanor, using classical and rabbinic evidence.
There are no sources that record the recitation of Hallel in the celebration of Yom Nicanor. The strongest evidence to indicate that it was said occurs in the Second Book of Maccabees (ch.15), one of the texts historically closest to the recorded event:
When the action was over and they were leaving with joy, they recognized Nicanor, lying dead, in full armor. Then there was shouting and tumult, and they blessed the sovereign in the language of the fathers...And they all decreed by public vote never to let this day go unobserved but to have the thirteenth day of the twelfth month, which is called Adar in the Syrian language, marked, the day before Mordechai's Day [i.e., Purim].
This is similar to 1 Maccabees 7:48:
And the people rejoiced exceedingly, and they spent that day with great joy.
Rejoicing and blessing Hashem "in the language of the fathers" sounds like Hallel, but there's no way of really knowing. Classical historians would likely argue against that idea, considering the increasing rift between the Pharisees and the Hasmoneans, who were supporting the Sadduccees (Samuel Rocca). Other classical sources, like Polybius Histories 31.22, either ignore the holiday, or they discuss Yom Nicanor as a day of celebration, but with no explicit mention of Hallel. Significantly, Josephus (Ant. 12.412) writes that people continued celebrating the holiday even after the Hasmonean dynasty was conquered:
And the Jews celebrate their victory every year in this month, and observe this day as a festival.
In my humble opinion, rabbinic sources seem to indicate that Hallel was not recited on Yom Nicanor. I have two explanations to corroborate this:
- None of the rabbinic sources available during the time of its celebration (Megillat Ta'anit, Talmud Bavli, Yerushalmi) mention a history of reciting Hallel during Yom Nicanor. The texts either discuss the story behind the holiday with detail or limit its rituals to a day when "one is not to fast and...not to eulogize."
- Yom Nicanor was still celebrated during the Gaonic period, even after Megillat Ta'anit was nullified, when the institution of reciting Hallel during a holiday was widely known. Masekhet Soferim discusses the issue of when to fast for Purim (before Ta'anit Esther was codified as the 13th of Adar):
נהגו להתענות אחר ימי הפורים, מפני ניקנור וחביריו
The custom is to fast after the days of Purim, because of Nicanor and his colleagues (17:3)
This text proves that Yom Nicanor had some status as a holiday during the Gaonic period. Nevertheless, three chapters later, Masekhet Soferim also records the 18 days and 1 night that we recite Hallel (20:7; see also Ta'anit 28b, where the Babylonian custom to recite Hallel on Rosh Chodesh is mentioned alongside the list), with no mention of Yom Nicanor. Although it's possible to argue that this shows no mitzvah to recite Hallel on Yom Nicanor, its absence from the Hallel list likely suggests that it was a minor holiday that people did not recite Hallel for.
If it was not practiced, there is not a lot of support for now instituting its recitation for Yom Nicanor during the years when Ta'anit Esther is displaced.