May people who are Menachem Avel eat food in the Shiva home?
Some are accustomed not to eat any food, or take any item, from the Shiva home throughout the seven days of Shiva. Others rule there is no need to be particular in this matter, and that so is the custom of many to eat food in the Shiva home after Shacharis. Some write that the custom to be stringent in this matter [according to the first opinion] only applies to the house in which the person passed away. However, if the person did not pass away in the Shiva house then there is no need to refrain from eating food in the home. [Practically, the widespread Ashkenazi custom is not to eat any foods in any Shiva house throughout Shiva. While the Sefaradi custom is on the contrary, to honor the visitors with food. Many Chabad Rabbanim have testified to this custom of avoiding eating in a Shiva home and that one is to abide by it. However, there are Chassidishe homes that offer the comforters food and drink. Seemingly, on Shabbos there is room to be lenient according to all.]
Lechaim: It is not our custom to offer a Lechaim in the Shiva home during the Shiva, with exception to on the seventh day, after Shacharis.
 See Nitei Gavriel 92/1
 Elya Raba O.C. 224/7; Rav Akiva Eiger 376; Beis Lechem Yehuda 376 that so is the custom in these provinces; Aruch Hashulchan 376/11; Mishmeres Shalom Mem/60; Keser Shem Tov p. 684; Kaf Hachaim 224/46
 The reason: As there is a spirit of impurity that resides in the house of the Avel throughout the seven days. [ibid]
 Yosef Ometz p. 330; Noheg Katzon Yosef p. 50; Ikarei Hadaat 34/30; Chaim Bayad 125; Yabia Omer 4/35; Nitei Gavriel ibid footnote 5; Nishmas Yisrael p. 130
 Nitei Gavriel ibid in name of Misgeres Hashulchan 376 and Even Yaakov 42
 Rav Eli Landa stated that his father was very careful in this matter, and so he saw accustomed amongst Chassidim to be careful; Rav Yeruslovsky stated the custom is to be stringent; Rav Gluchovsky stated the Chabad custom is to be stringent; Rav A.L. Hakohen told me the custom in all Ashkenazi circles is to be stringent in this.
 Nitei Gavriel ibid footnote 5; Rabbi Leibal Groner in a correspondence related that he witnessed in many Chassidishe homes to offer Lechaim and Mezonos after Shacharis.
 See Shivlei Haleket 23 that the adherence of not drinking form the cup of an Avel does not apply on Shabbos; See Nitei Gavriel ibid footnote 21
 See Toras Menachem-Reshimos Hayoman p. 414 that the Rebbe Rayatz instructed the Rebbe to have Lechaim distributed only on the 7th day. See Shulchan Menachem 5/282 footnote 5