Thus, fasting and saying kaddish on a parent’s yahrzeit are observed in Adar Rishon. The yahrzeit date in Adar Sheni is treated with lesser observance; one recites kaddish but does not fast. (There is an opinion in Piskei Mahari, cited by the Rema, however, that one fasts on both days.)
The 12 months of mourning start at the time of death. If the person is not buried the same day he died, there is a major dispute among the authorities regarding when to observe the yahrzeit. The Shach (Yoreh De’ah 402:12, citing the Responsa of R. Binyamin) rules that if the burial is not on the same day as the death, or on the following day, then the first yahrzeit follows the date of burial, as there must be a complete 12 months of mourning, and in this case three days would be missing.
The Taz (ad loc. and Orach Chayyim 568:8) disagrees, saying: “If one first heard of the death of his father six months after his death, there is no one who would rule that he now mourns for 12 months from the time he heard about it, but rather the 12 months are counted from the time of the date of death.”
In practice, we seem to follow the ruling of the Shach, but only if three complete days have passed (see Yesodei Semachot, the excellent sefer by R. Aron Felder, shlita, of Philadelphia). In every year after the first one, though, yahrzeit is observed on the day of death. This is inferred from the Gemara (Shevuoth 20a) and Rashi (ad loc. s.v. “Keyom she’met bo aviv”), where we see that the date of death is imbued with a precision clear enough to effect a proper oath.
Now, concerning Purim, we find the following statement in the Mishnah (Megillah 6b): “There is no difference between the first Adar and the second Adar except for the reading of the Megillah and matanot l’evyonim.” The Gemara explains that just like eulogies and fasting are forbidden on the 14th and 15th day of Adar Sheni, so too are they forbidden on the 14th and 15th of Adar Rishon.
The Mechaber and Rema (Orach Chayym 697:1) note a different view but set the halacha like the Gemara we just mentioned. Eulogies and fasting are forbidden on Purim and Shushan Purim of both Adars since Adar is a time when “we increase our joy” – marbim b’simcha.
The famed Rabbi Levi Yitzchak of Berditchev writes (Sefer Kedushat Levi on the end of parashat Ki Tissa): “The reason that Adar is the month we intercalate…is because it is well known that the twelve months of the year are representative of the twelve tribes of Israel, as cited by the Tur (Orach Chayim 417). Now, the month of Adar, whose mazal is Pisces [fish], is representative of Joseph, who is compared to the fish upon whom the evil eye has no power [as they are hidden in the water]. As the verse in Parshat Vayechi (Genesis 49:22) states, ‘Ben porat Yosef ben porat alei ayin – A charming son is Joseph, a charming son to the eye.’ [Our sages interpret this verse to mean that Joseph and his progeny are protected from the evil eye – Berachot 20a.] Joseph bore two of the tribes, Menashe and Ephraim [who are considered individual tribes, as it says (Genesis 48:5), ‘Ephraim and Menasseh shall be mine like Reuben and Simeon’]. Therefore there are two Adars.”
Levi is not counted among the tribes that were allotted portions in the land or had their own flags and encampments in the desert. Deuteronomy 10:9 states: “Al kein lo hayah l’Levi chelek v’nachalah im echav, Hashem Hu nachalato ka’asher diber Hashem Elokechah lo – Therefore, Levi did not have share and a heritage with his brethren, the L-rd is his [portion].” However, in regards to the mazalot, Levi is counted amongst the twelve tribes and Joseph is counted as only one tribe.