1. Isru Chag:
The day after each of the three Holidays is called Isru Chag. The name Isru Chag derives from the verse “Isru Chag Baavosim Ad Karnei Hamizbeiach”. This means to say that this day is to be attached [i.e. Isru] to the Holiday itself, and by doing so the verse considers him to have built an Altar and sacrificed on it an offering. For this reason the following customs are relevant on Isru Chag:
B. Fasting on Isru Chag:
It is forbidden to fast on Isru Chag, the day after each of the three festivals. Even a Chasan and Kallah which are getting married on Isru Chag [as they follow the customs of Sefirah only after Rosh Chodesh] are not to fast that day. Similarly, a child may not fast on his parent‘s Yartzite that falls on Isru Chag.
One is to increase a little in eating and drinking on Isru Chag. Even a Chasan and Kallah on the day of their wedding may not fast on this day. Similarly, a child may not fast on his parent‘s Yartzite.
Do the customs of Isru Chag apply also on the night after [i.e. Motzei] Isru Chag?
Some Poskim write that the customs of Isru Chag [increasing in food and drink] apply also to the night after, which is Motzei Isru Chag.
Sparks of Kabalah:
The Arizal taught that on the day after Yom Tov, Isru Chag, a ray of the Holiday still shines.
2. May one eat Chametz after Pesach prior to the conclusion of the return sale?
One may begin eating Chametz immediately after the conclusion of Pesach, even though it is prior to the return sale of the Chametz taking place with the gentile. Doing so does not border on stealing from the gentile or any other transgression. This especially applies in those sale contracts that make an explicit stipulation with the gentile that one may eat the Chametz prior to the conclusion of the return sale. [Practically, so is explicitly written in the sales contracts of the Eida Hachareidis and of Rav Landa of Bnei Brak. Others however do not explicitly write this stipulation.] Even by those sale contracts that do not explicitly make this stipulation, one may be lenient to allow one to eat the Chametz prior to the end of the sale if one knows for certain that the gentile is not particular on this matter. Practically, it is proper for every Rav who is arranging a sale contract to enter this stipulation explicitly in the contract and hence merit the public. Alternatively, the Rav is to arrange to purchase back the Chametz immediately after Pesach.
Eating Chametz during one’s last Pesach meal: One whose meal on the last day of Pesach continued into Motzei Yom Tov, until after Tzeis Hakochavim, is now permitted to eat Chametz during his meal [prior to Birchas Hamazon] even though he did not yet Daven Maariv or recite Havdala at all [and did not even say Baruch Hamavdil]. [In such a case, one is nevertheless to recite Yaaleh Veyavo and Chag Hamatzos Hazeh within his Birchas Hamazon.]
 Admur 429/17
 429/17; Sukkah 45b
 Admur ibid; Rama 429/2
 429/17; Rama 429/2; Sukkah 45b based on second explanation of Rashi ibid [according to his 1st explanation, the Mitzvah is to increase on Yom Tov itself, and not the next day]
 The reason: Anyone who attaches [Lit. Issur which means bound] the day after the festival to the festival itself with eating and drinking, meaning through increasing slightly in eating and drinking the day after the Holiday, and thus makes that day attached [Lit. Tafal which means secondary, or attached] to the Holiday itself, the verse considers him to have built an Altar and sacrificed on it an offering. This is based on the verse that states “Isru Chag Baavosim Ad Karnei Hamizbeiach”. Meaning to say that when one makes an Issur, a secondary day, to the festival, then Baavosim, it is considered as if he brought large and fat animals to the altar. For this reason the custom is in these provinces to increase a little in eating and drinking on the day after each of the three festivals. [Admur ibid; Sukkah ibid]
Other reasons: Some write that the celebration of Isru Chag began in Eretz Yisrael in order to show some sign of festivity on the second day of the festival of the Diaspora. This then dspread to the Diaspora itself, on their Isru Chag. Alternatively it corresponds to the sacrifices which were able to be eaten for two days and one night. [Sdei Chemed Kelalim Alef 154] Alternatively it is in memory of the pilgrimage which would return home on Isru Chag. [Glosses of Chasam Sofer 429]
 429/17; M”A 429/8
 Custom or prohibition? The above prohibition however is only a custom, however from the letter of the law there is no prohibition to fast, although one who refrains from doing so is praised. [Admur ibid; M”A 429/8] This however only applies to the day after Pesach and Sukkos, however on the day after Shavuos from the letter of the law it is forbidden to fast. [Admur 429/18] The reason for this is because on the night of Isru Chag of Shavuos all the sacrifices of the pilgrimage were offered in the Temple, and it was thus made a festival. [494/19; Seemingly according to this also Erev Pesach should be forbidden from the letter of the law, being that all the peach sacrifices were brought then. However in 429/10 it is not mentioned in the list of days that are prohibited from the letter of the law to fast. Vetzaruch Iyun. The practical ramification is in whether one may make up a Taanis Chalom on that day.]
A Taanis Chalom: It is certainly permitted to fast a Taanis Chalom on Isru Chag, as even o9n Shabbos it is permitted. Nevertheless Tzaruch Iyun if such a fast requires a second fast as a Kaparah.
 Admur ibid; M”A 573/1
 Admur ibid; Rama 429/2 regarding all days of Nissan; See also Rama 568/9
Fasting on the Yartzite of parents on other days in Nissan: From here it is implied that one may fast on a Yartzite on the remaining days of Nissan. This is unlike the Rama 429/2 which rules a Yartzite fast may not be done at all during Nissan. Admur in 429 omits this ruling of the Rama.
 Ashel Avraham of Butchach 429
 The reason: As this is similar to Kodshim in which the night follows the day in terms of the burning of the offerings from the sacrifice. [ibid]
 Torah Leshma 140; Darkei Chaim Veshalom 524
 The reason: This is done in order to actively show the continued Holiness of the festival that is relevant to this day, and so one does not treat it like a regular weekday. [Torah Leshma ibid]
 Torah Leshma 140
 Rav Avraham Chaim Naah [brought in Yagdil Torah Yerushalyim 6/2610]
 Grac”h Naah ibid; Yechaveh Daas 2/64; Vaad Hakashrus of Eida Hachareidis [via phone call]; Vaad Hakashrus of Rav Landau [Via correspondence with Rav Eli Landau]; See Choshen Mishpat 359/1-2; Admur Hilchos Gezeila Ugineiva 1-2;
Other Poskim: The Or Yisrael 447/4 in name of the Gaon of Butchach allows taking the Chametz only in a) a case of great need and b) one does so before two witnesses; The Aruch Hashulchan 448/28 writes that the Rav is to buy back the Chametz immediately after Pesach, prior to the storekeepers opening their store, hence implying that prior to the sale one may not take the Chametz, and so concludes Nitei Gavriel 60/1. He however makes no mention of any of the above Poskim that rule it is permitted.
 Grac”h Naah ibid
The reason: One may eat the Chametz immediately after Havdala even if the Chametz was not yet bought back and doing so contains no worry of transgressing stealing from the gentile as the gentile does not care if one eats the Chametz before the return sale. However this only applies if one takes the Chametz with intent to pay the gentile back for its market value, if in truth the gentile chooses to keep the Chametz and not go through with the return sale. Obviously if one would not agree to these terms then it would be considered stealing from him, as in this case he is particular against coming to a loss. [Grac”h Naah ibid] This is based on the law regarding taking an item from a person without his permission which is dependent on whether we assess that the owner is particular or not. [See Choshen Mishpat 359/1-2; Admur Hilchos Gezeila Ugineiva 1-2] Thus in this case certainly the owner is not particular, as the whole purpose of his bought Chametz is to be sold for market value, and thus when the Jew takes it with intent to pay the gentile back he is actually meriting the gentile, and the rule is Zachin Leadam Shelo Befanav. Now, although in Choshen Mishpat ibid this allowance only applies if one “acquires the payment to the owner through another person” [Michaber 359/2; Smeh 359/8; Admur 2] nevertheless perhaps here one may be lenient as the gentile himself [through the Eruv Kablan] himself must pay the Jew for the Chametz that he purchased, and hence in conclusion when the Jew takes it without permission, it evens out the debt of the gentile to the Jew. Nonetheless, the Or Yisrael ibid states that due to these issues it is only initially permitted to take the Chametz if one does so in front of two witnesses. See Grac”h Naah ibid; In addition to all the above, see Kuntrus Achron 440/11 that there is no prohibition against stealing from a gentile when one intends to return the itemץ
 Grac”h Naah ibid; Yechaveh Daas 2/64; See Shaarey Halacha Uminhag 2/195 which also makes mention of such a stipulation for the help of selling Chametz of a Jew which is not observant and may take the Chametz on Pesach; See however “Seder Mechiras Chametz” p. 178 of Rav S.D Levin which states that this condition established by the Rebbe only applies to the sales contract of the store, and not to the general sale contract.
The benefit of this stipulation: Making the stipulation explicit in the contract avoids all worries and issues that were discussed in the previous footnote. [Grac”h Naah ibid]
 This stipulation was placed by Rav Avraham Chaim Naah, who was the secretary of the Eida Hachareidis at that time. The stipulation was brought to the attention of Rav Bengis who was the Chief Rabbi of the Eida Hachareidis at that time, and he praised the idea.
 In the words of Rav Eli Landau “Every [respectable] Rav of all generations made this stipulation both orally and in writing with the gentile, in order to allow the Jew to take the sold medicine if he so needs. The gentile gives explicit permission to the Jew to take the Chametz before it is sold back on condition to pay him for it.”
 The contract of Rav Ashkenazi of Kfar Chabad does not contain this stipulation, and neither does the contract written by Rav Levin in his Seder Mechiras Chametz.
 See Choshen Mishpat 359/1-2; Admur Hilchos Gezeila Ugineiva 1-2 and “The reason” brought in previous footnotes for an explanation of this matter. Practically, while the Grac”h Naah seems to side there is no issue with taking the Chametz even if it was not stipulated in the contract he explicitly records the Or Yisrael ibid that allows doing so only in front of two witnesses.
 Grac”h Naah ibid; Rav Eli Landa ibid
 Aruch Hashulchan 448/28
 Admur 491/3; M”A 491/1 [Begins with Tzaruch Iyun, although gives reason to conclude that it is Mutar]; Chok Yaakov 491/1 [concludes like suggestion on M”A ibid]; Elya Raba 491/1; Chok Yosef 491/1; Shulchan Gavoa 491/1; Poskim in Kaf Hachaim 491/7; See Likkutei Sichos 22/36 footnote 62-64
Other opinions: Some Poskim rule one may not eat Chametz prior to reciting Havdala. [P”M 491 A”A 1; See Kaf Hachaim ibid] Other Poskim rule that while one may rely on the Poskim ibid to eat Chametz prior to Havdala, one may not eat Chametz prior to reciting Birchas Hamazon, being that this will create a contradiction to his recital of Yaaleh Veyavo in Birchas Hamazon, as how can he say Chag Hamatzos Hazeh if he ate Chametz. [M”B 491/1; See Kaf Hachaim 491/8 and Likkutei Sichos ibid who negates this understanding, as it is forbidden to eat after Birchas Hamazon, prior to Havdala, and hence the only case in which the Poskim ibid can possibly allow eating Chametz is if one did not yet say Havdala.]
 Pashut; Kaf Hachaim 491/8; Likkutei Sichos ibid; See previous footnote!
 So is implied from the wording of Admur “and did not yet say Havdala at all”
 The reason: As the prohibition against eating Chametz on Pesach is not dependent on Havdala at all, and since Tzeis Hakochavim has arrived, it is considered night for all matters, and the holiness of Yom Tov has already dissipated. The fact that one is prohibited from doing Melacha prior to Havdala is not due to the holiness of the Yom Tov, but rather due to a Rabbincial prohibition due to reasons explained in 299/15. (Now, although there is a Mitzvah to add onto the Holiness of Yom Tov, this is only with regards to not doing Melacha during the additional time of Yom Tov, as this Mitzvah is learned from the verse “Tishbisu Shabatchem”, as explained in 261/4.) However, regarding other matters which are dependent on the holiness of the day, such as the Mitzvah of Mikra Kodesh, see chapter 529, there is no need to add from the weekday to the Yom Tov. Accordingly, certainly the eating of Chametz, which is not dependent at all on the holiness of the day, as even during Chol Hamoed one is prohibited from eating Chametz, [is permitted to be eaten during the period of Tosefes Yom Tov]. [Admur ibid]
 Implication of M”B ibid; Kaf Hachaim 491/8 in name of Poskim; Likkutei Sichos ibid