What was the celebration of the 10th of Adar? Why would the pagan worshipers base a holiday based on a Jewish date?
The Gemara and commentaries do not expand on the nature of any of the various pagan celebrations mentioned in this Gemara.
The names of the months that we are accustomed to using (Nisan, Iyar etc.) are not the month's Hebrew names. They are Persian names that the Jews adopted during the Babylonian exile, according to the Yerushalmi (Rosh Hashanah 1:2). Apparently, the Persian calendar in use at the time was a lunar one, similar to ours.
Only a few of the original Hebrew names of months are mentioned in scriptures, such as "Ziv" and "Eisanim" (see Rosh Hashanah 11a)