Having gentile guests Yom Tov:
It is forbidden to invite gentile guests for a Yom Tov meal. This applies even if all one’s food is already cooked. If, however, the gentile arrived on his own, one may give him food to eat, although it is forbidden to invite and press on the gentile to eat [if he does not accept the initial offer].
Housemaid: 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.
 See Admur 512:1-3; Kaf Hachaim 512:5-15
 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]
 Admur 512:2; Taz 512:4; See Kaf Hachaim 512:5
 Admur 512:2; Michaber ibid; Beitza ibid
 See Kaf Hachaim 512:5
 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]
 Admur 512:3-4; Michaber and Rama ibid