Background of Pesach Sheiyni:
In the times of the Temple, a person who did not bring the Pesach offering in the 14th of Nissan, either due to being impure or due to being a distance from Jerusalem, was required to bring the offering a month later, on the 14th of Iyar. [Accordingly, it is customary to celebrate this day as a Holiday.]
The Name Pesach Sheiyni:
The name Pesach Sheiyni is used in the Mishneh Pesachim 9/3. Another name is Pesach Zeira or Pesach Katan, which means the small Pesach.
Increasing in Simcha:
One is to increase in joy out of the holiness of the day.
Learning the laws of Pesach Sheiyni:
It is proper to learn the laws of Pesach Sheiyni on the 14th of Iyar.
Tachanun [and Lamnatzeiach and Keil Erech Apayim] is omitted on Pesach Sheiyni, which is the 14th of Iyar. It is however recited the Mincha prior, on the 13th of Iyar. [Thus when the 13th falls on Shabbos, Tzidkascha is recited by Mincha.] Tachanun is likewise omitted on the night of the 14th in Kerias Shema Sheal Hamita. It is questionable whether it is to be recited on Motzei Pesach Sheiyni, which is the night of the 15th. [However, on the day of the 15th Tachanun is recited.]
Erev Pesach Sheiyni: It is permitted to eulogize and say Tziduk Hadin on Erev Pesach Sheiyni even past midday.
May a Matzeiva [tombstone] be established on Pesach Sheiyni?
This may not be done if eulogies will take place during the occasion.
One is not to fast on Pesach Sheiyni, as is the law regarding any day in which Tachanun is omitted. This applies even if the fasts of Bahab fall on this day. Some Poskim however allow fasting on this day, especially if the fast of Bahab falls on the 14th of Iyar.
It is customary to eat Matzah in honor of Pesach Sheiyni.
When? Many are accustomed to eat Matzah on Pesach Sheiyni, on the day of the 14th of Iyar. Some are accustomed to eat it towards the afternoon. Others are accustomed to eat Matzah [only or also] on Motzei Pesach Sheiyni, which is the night of the 15th of Iyar. Others eat on the night of the 14th. Those that are most scrupulous eat Matzah all three times.
The Chabad custom: Our custom is to eat Matzah during the day meal of the 14th of Iyar. The Rebbe himself however ate the Matzah many years on the night of the 15th. This custom is also mentioned in talks of the Rebbe. As stated above, the Rebbe states that those who are meticulous eat Matzah three times, once on the night of the 14th, once by the day of the 14th, and once on Motzei the 14th.
May one say “This meat is for Pesach Sheiyni”?
One is to avoid doing so.
May one eat roasted meat on Pesach Sheiyni?
Some Poskim rule one is to avoid eating roasted meat on Pesach Sheiyni. Others however rule this stringency only applies to roasting a whole lamb or goat.
Maror and a cooked egg:
Some are accustomed to eat Maror and a cooked egg on Pesach Sheiyni.
 Rambam Karban Pesach 5/1
 Siddur Yaavetz
 Megillas Taanis 2
 Moreh Baetzba 8/222; Moed Lekol Chaiy 7/6
 Shlah; Kaf Hachaim 489/6; Mentioned in Sichas of Rebbe brought in Otzer Minhagei Chabad 44
 Siddur Admur; Siddur Shlah; Elya Raba 131/14; Shalmei Tzibur p. 151; Siddur Yaavetz; Shaareiy Efraim 10/27; Shaareiy Teshuvah 131/19; Ashel Avraham Butchach 131; Divreiy Nechemiah 131; Kaf Hachaim 131; Not listed in Shulchan Aruch Chapter 131. See Aruch Hashulchan 131/12 and Yalkut Avraham 493 who wonders at this matter.
Other Opinions: Some Poskim rule that Tachanun is to be recited on Pesach Sheiyni. [P”M 131 M”Z 14; Noam Megadim 26; custom of Chazon Ish; This was the widespread Ashkenazi custom] It is interesting to note that one of the main claims of the Misnagdim against the Chassidim in the Cherem of 1772 was that they did not say Tachanun on Pesach Sheiyni, and held feasts on the day even when it fell on Behab. [Nitei Gavriel Pesach 3 57/3]
 Piskeiy Hassidur 151 and 179; Sichas Kodesh 6th Tishrei 1975 based on Admur in Siddur that Lamnatzeiach is never recited when Tachanun is omitted. This ruling in the Siddur is based on Kneses Hagedola 131/3; Peri Chadash 131/1; Mamar Mordechai 131/6; Kaf Hachaim 581/78 states that so is the custom of the Sefaradim.
Ruling of Admur in the SHU”A: In the Shulchan Aruch, Admur rules like Rama 131/1 that Lamnatzeiach may be recited even on a day that Tachanun is omitted. [Admur 429/12; 602/4 [in parentheses]]
 Siddur Tehillas Hashem [from 1978 and onwards with the Rebbe’s approval] based on Sichas Kodesh 6th Tishrei 1975 that the Rebbe equates Kel Erech Apayim with Lamnatzeiach. See Shulchan Menachem 3/293; Glosses of Rav Raskin p. 165; Hiskashrus 438 p. 17; To note however that the Rebbe himself did recite Kel Erech Apayim even when Tachanun was not recited. [Rav Raskin ibid]
Ruling of Admur: In the Shulchan Aruch [429/12; 602/4] Admur rules that Kel Erech Apayim is recited with exception for Erev Pesach. This follows the ruling of the Hagahos Maimanis; Darkei Moshe 602 brought in Kaf Hachaim 602/12. [Some explain that it is for this reason that Admur in 602/4 placed this ruling in parentheses, as it is not brought in previous Poskim in Shulchan Aruch. [Shulchan Menachem ibid footnote 2] Vetzaruch Iyun as it is brought by Admur in 429/12 without parentheses, and is likewise clearly implied from the Rama 429/2] To note that also in the Siddur before Kel Erech Apayim Admur lists a number of days that it is to be omitted on, thus implying it is not always omitted when Tachanun is not said.
Ruling and explanation of Divrei Nechemia: The Divrei Nichemia 131/9 brings three opinions regarding the saying of Keil Erech Apayim:1) It is only omitted by a day that Halel is recited or a day that has the status of a Yom Tov like Erev Pesach. [This is the opinion of the Rama 429/2] 2) It is omitted on every Erev Yom Tov and on Isru Chag. 3) Every day that Tachanun is omitted so is Lamnatzeiach. [so rules Peri Chadash 131] The Divrei Nechemia concludes that by Lamnatzeiach we rule like the third opinion, however by Keil Erech Apayim we rule like the opinion that rules it is to be recited.
The reason behind the Rebbe’s ruling: The Rebbe explains that the ruling in the Shulchan Aruch of Admur follows the ruling of the Rama that differentiates between the laws of Tachanun and that of Lamnatzeiach. However according to Admur in the Siddur that rules Lamnatzeiach is always omitted when Tachanun is not said then likewise Kel Erech Apayim is to be omitted in all days that Tachanun is not said. [Sichas Kodesh ibid, printed in Shulchan Menachem ibid] As for the reason why Kel Erech Apayim is omitted this is because it mentions sin, and we do not desire to mention sin on any day that Tachanun is omitted. [See Shaar Hakolel 36/2; Shulchan Menachem ibid footnote 5]
 Siddur Admur; Divreiy Nehemiah 131; Hayom Yom 13th Iyar
Other Opinions: Some Poskim rule that Tachanun is omitted also from the Mincha prior. [Shaar Yissachar Pesach Zeira in name of Arizal; Nitei Gavriel 57/4 in name of Sefarim; Siddur Arizal Chemdas Yisrael]
 Hiskashrus 1033
 Sichas 1983 Pesach Sheiyni letter 12; Behar Bechukosaiy 1983 letter 42; See Otzer Minhagei Chabad Iyar 42
 Machazik Bracha 131/4; Beis David 53; Shaareiy Teshuvah 131/19; Rebbe ibid based on Siddur Admur
Other opinions: Some are accustomed not to say Tachanun also on the 15th. [Shalmei Tzibur p. 151; See Otzer Minhagei Chabad p. 267; Regarding the opinion of the Munkatcher, in Darkei Chaim Veshalom 191 it states that he did not say Tachanun on the 15th and in Nimkei Orach Chaim 131/6 and in Shaar Yissachar [Pesach Zeira] he writes that according to the students of the Arizal it is to be omitted. The Rebbe ibid however explains that most likely the Munkatcher held Tachanun is omitted by the night of the 15th and not the day.]
Custom to omit Tachanun for seven days: Some are accustomed to omit Tachanun for seven days until the Tashlumin of Pesach Sheiyni expires. [Likkutei Maharich in name of Hayashar Vehatov of Liska; Custom of Divrei Chaim and Tzanz; See Piskeiy Teshuvos 492/1 footnote 8] Others negate this custom. [Darkei Chaim Veshalom 191; Nimkei Orach Chaim 131/6; Shaar Yissachar [Pesach Zeira]]
 Megilas Taanis “Pischa Zeira is forbidden in eulogy”; See Michaber 420/1 and 670/3 and Y.D. 401/5; Taz 420/1; M”A 420/1 and 548/8; Admur 429/8 regarding the month of Nissan; Chochmas Adam 169/25 [unlike Chayeh Adam 118/7]; Kaf Hachaim 420/1; Nitei Gavriel Aveilus 52/3
 This law if learned from the law brought in Poskim ibid that women do not lament by funerals during these days. It is also learned from the Poskim in next Halacha who prohibit saying Tziduk Hadin on any day that Tachanun is omitted, and if Tziduk Hadin is omitted than certainly a Hesped may not be said. [See Taz ibid that a Hesped is more severe than Tziduk Hadin as Tziduk Hadin is “not a eulogy but recognition and acceptance of the Divinje decree” and hence some opinions allow Tziduk Hadin; See also M”A 548/8 that one may not even say praise of the dead because this can lead to a eulogy.]
 Michaber Y.D. 401/5; See Admur ibid; Taz and M”A ibid; Chochmas Adam 169/25 [unlike Chayeh Adam 118/7]
 Rama 420/2 and Y.D. 401/6; Maharitz Geios; See Kaf Hachaim 420/2
Other opinions: Some Poskim rule that Tziduk Hadin and Kaddish is recited on Lag Baomer being it is not considered a eulogy but merely a blessing to Hashem. [Michaber 420/2; Opinions in Tur 420; Talmidei Rashi; Rambam] Practically, each community is to follow their custom, and in a place where there is no set custom, it is better not to say it. [Kaf Hachaim ibid]
 Taz 420/1 that the Rama passed away on Lag Baomer of the year 5333 [שלג] and they were in question as to whether they should say Tziduk Hadin, at which point a prestige Sage stepped forward and stated that he heard from the Rama that one may say Tziduk Hadin on an important Sage, and so he went ahead and said it in a loud voice. [Taz ibid]
 This applies according to all opinions being that Tachanun is not omitetdfrom Mincha of the 13th.
 See Sefer Haminhagim p. 20 and 68 [English]
 Darkei Chaim Veshalom 634; See P”M 108 in M”Z and 671 M”Z 8; Minhagei Chasam Sofer 1/14; Biur Halacha 132
 See Maharsham 2 Hakdama [established a Matzeiva for his wife on Lag Baomer]; Dvar Yehoshua 1/80; Minchas Yitzchak 3/51-53 in name of Levushei Mordechai and 4/107; Kinyan Torah 2/122; Nitei Gavriel 16/3; Piskeiy Teshuvos 697/1
 Yosef Daas Veyad Shaul Y.D. 401; Likkutei Maharich; See M”A 573/1; P”M 568 A”A 19; M”B 568/37 and 573/7; Ashel Avraham Butchach 573 that one does not fast on any day that Tachanun is omitted; See Megilas Taanis ibid that a Hesped is forbidden on Pesach Sheiyni, and the same would apply to a fast
 Yosef Daas Veyad Shaul Y.D. 401; Likkutei Maharich; It is interesting to note that one of the main claims of the Misnagdim against the Chassidim in the Cherem of 1772 was that they did not say Tachanun on Pesach Sheiyni, and held feasts on the day even when it fell on Behab. [Nitei Gavriel Pesach 3 57/3]
 Maharsham 6/42; Siddur Yaavetz ; Ashel Avraham Butchach, brought in Taamei Haminhagim p. 250; Custom of Chazon Ish
 M”A 573/1; Chayeh Adam 132/43; Kitzur SHU”A 146/2; M”B 573/7
 Elya Raba 573/3 in name of Nachals Shiva; M”B ibid in name of Yeish Makilim; Mishmeres Shalom 38/3; Ashel Avraham Butchach ibid
 Mateh Efraim 625/2; Daas Torah 573; Piskeiy Teshuvos 493/9
 Siddur Yaavetz; Darkei Chaim Veshalom 531-532 that so was the custom of all the students of the Baal Shem Tov; Shaar Yissachar Pischa Zeira 12; Poskim recorded in Nitei Gavriel 57 footnote 13 and that so is the worldly custom; Igros Kodesh 2 p. 352 [however see footnotes below]
Other opinions: Some do not eat Matzah at all on Pesach Sheiyni. [Maaseh Rav 181; Revivos Efraim 2/129 that so was the custom in Lita; The Chazon Ish did not eat Matzah on Pesach Sheiyni, brought in Nitei Gavriel 57 footnote 15]
 The reason: The Yaavetz writes that he was revealed from Heaven that the holiness of Pesach and Matzah continue until Pesach Sheiyni.
 Igros Kodesh 2 p. 352 [however see footnotes below]; Siddur Beis Yaakov; Darkei Chaim Veshalom 631-632 that so was the custom of all the students of the Baal Shem Tov; Shaar Yissachar Pischa Zeira 12; Poskim recorded in Nitei Gavriel 57 footnote 13 and that so is the worldly custom.
The reason: As the sacrifice of the Pesach offering occurred on the 14th. [Darkei Chaim Veshalom ibid]
 Rebbe in Sichas Shemini 1980 28; Nitei Gavriel ibid
 Likkutei Mahrich 44; Piskeiy Teshuvos 492/1 footnote 10; The Rebbe’s custom of many years as recorded by Rav Groner; In a list of Sichas the Rebbe mentioned the custom to eat Matzah on the night after the 14th. [See Otzer Minhagei Chabad Iyar 44]
The reason: As the meat of the Karban Pesach was only eaten on the night of the 15th.
 Darkei Chaim Veshalom ibid
 Rebbe in Sichas Shemini 1980 28; brought in Otzer Minhagei Chabad 44
 Igros Kodesh 2 p. 352 based on the custom of the Rebbe Rayatz; Hiskashrus 1033
 Rabbi Leibal Groner
 Piskeiy Teshuvos 492/1
 Piskeiy Teshuvos 492/1
 Rashash Pesachim 53a
 Chazon Ovadia 2/175
 Darkei Chaim Veshalom ibid; Piskeiy Teshuvos 492/1 footnote 11