The Mitzvah:

When one eats and drinks on Yom Tov, he is obligated to feed converts, orphans and widows, amongst all other unfortunate paupers. One who locks the doors of his home and eats and drinks with his wife and kids alone and does not feed give drink the paupers and people of misfortune, their meal is not considered a Simchas Mitzvah, but rather a Simcha of tehri stomachs. On this the verse states that their bread is impure, and it is as if they have placed manure on their face. This form of joy is considered a mockery of themselves.   

Having gentile guests Yom Tov:^[1]

It is forbidden to invite gentile guests for a Yom Tov meal.^[2] This applies even if all one’s food is already cooked.^[3] If, however, the gentile arrived on his own, one may give him food to eat^[4], although it is forbidden to invite and press on the gentile to eat [if he does not accept the initial offer^[5]].^[6]

Housemaid:^[7]  It is permitted to have a gentile housemaid eat the Yom Tov meals with one’s family and to even add more food to the pot prior to placing it on the fire, so long as one does not cook an extra pot of food just for her.

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[1] See Admur 512:1-3; Kaf Hachaim 512:5-15

[2] Admur 512:1; 325:1; Michaber 512:1; Beitza 21b

The reason: It is forbidden to invite gentile guests on Yom Tov due to a decree that one may come to cook another pot of food on behalf of the gentile, and Meleches Ochel Nefesh was only permitted to be done on Yom Tov on behalf of a Jew and not on behalf of a gentile. [Admur ibid; Taz 512:2]

[3] Admur 512:2; Taz 512:4; See Kaf Hachaim 512:5

[4] Admur 512:2; Michaber ibid; Beitza ibid

[5] See Kaf Hachaim 512:5

[6] Admur ibid; Taz 512:4

The reason: It is permitted to offer him to eat if he has arrived uninvited is in such a case there is no worry that one may be pressured into cooking him a separate pot of food as one is not pressed to honor and respect him. However, it is forbidden to oppress upon the gentile to eat by him as this shows that he is trying to honor him and we thus suspect that he may come to cook something else on his behalf. [Admur ibid]

[7] Admur 512:3-4; Michaber and Rama ibid

[8] Minchas Yitzchak 2:118; Piskeiy Teshuvos 512:1

[9] Admur O.C. 39:1 “He is like a gentile for all matters”; Michaber Yoreh Deah 2:5 “He is like a gentile”; Admur Y.D. 2:10 “He is a like a gentile regarding Shechita and for the entire Torah, except for Kiddushin”; Rashba 7:53; Tiferes Lemoshe 113:9 [brought in Pischeiy teshuvah 113:1] regarding Bishul Akum [however not Pas Akum]; Erech Hashulchan 112:2; Kaf Hachaim 112:11; Ketzos Hashulchan 101:5 and Kitzur Shulchan Aruch 72: “Anyone who publicly desecrates Shabbos is considered like an idle worshiper and [thus] if he touches wine he forbids it, and the bread which he bakes is like Pas Akum, as well as the food which he cooks is like Bishul Akum.”

[10] Mabit 1:38 in name of Rabbeinu Shimshon; P”M 512 A”A 1 and M”Z 1; M”B 512:2; Kaf Hachaim 512:4

[11] Yearos Devash end of volume 1

[12] Maharam Shick 281 that so is opinion of Maharashach brought in M”A 512:1 regarding the Karaim; See P”M ibid

[13] See M”A 512:1; M”B 512:2; Kaf Hachaim 512:3

[14] Reb Betzalel 63 in name of Radbaz; 1^st opinion in M”A 512:1, Kneses Hagedola 512, Elya Raba 512:1, M”B 512:2

[15] Maharshach 3:15; 2^nd opinion in M”A 512:1, Kneses Hagedola 512, Elya Raba 512:1, P”M 512 A”A 1, M”B 512:2