Gemara

A slave does not eat in front of his master. Therefore, it is less proper to eat in a more Kadosh place

Megilah 28b (Beraisa): We do not conduct frivolously in Batei Kenesiyos. We do not eat or drink there. We do not enter a Beis ha'Keneses to avoid heat or rain.

Rav Asi: Batei Kenesiyos in Bavel are made on Tanai (a stipulation). Nevertheless, we do not act in them frivolously, i.e. to make calculations;

Rava: Chachamim are permitted.

Rava was teaching Ravina and Rav Acha bar Masnah. A torrential rain came; they entered a Beis ha'Keneses. They did not enter to avoid the rain, rather, for the sake of learning, which requires clarity.

Pesachim 101a: Shmuel requires Kidush to be in the place where one eats. He holds that we make Kidush in the Beis ha'Keneses for visitors who eat, drink and sleep in the Beis ha'Keneses. They are Yotzei through it.

Sanhedrin 70a (Mishnah): The meal of Ibur Chodesh (to signify when a 30th day was added to a month) is a Seudas Mitzvah.

70b (Beraisa): In the meal of Ibur Chodesh they bring only bread of grain and legumes.

Bava Basra 3b: Rav Ashi saw cracks in the Beis ha'Keneses of Masa Nachsiya. He destroyed it, and moved his bed there (to make people zealous to build it quickly).

Rishonim

The Rif and Rosh (Megilah 9a and 4:7) bring the Gemara in Megilah. Their text of the Beraisa discusses Batei Kenesiyos and Batei Medrashos.

Rif and Rosh (Pesachim 19b and 10:5): Kidush in the Beis ha'Keneses is Motzi visitors who eat, drink and sleep there.

Ran DH Le'afukei): Even though we do not eat or drink in a Beis ha'Keneses, perhaps for visitors it is considered a Mitzvah of the Rabim, for they are fed by the Tzedakah box of the city. Alternatively, they eat in rooms next to the Beis ha'Keneses.

Rambam (Hilchos Shabbos 29:8): We make Kidush in the Beis ha'Keneses to be Motzi visitors who eat there.

Magid Mishnah: The visitors hear Kidush and eat in houses next to the Beis ha'Keneses, for one may not eat in a Beis ha'Keneses.

Hagahos Maimoniyos (5): This is unlike Rashi (28b DH Tanai), who says that the Tanai allows benefit from them (even while they are in use). One may eat and sleep in a Beis ha'Keneses for the sake of Mitzvos.

Ran (DH Batei): The Ramban explains that the Tanai allows the city to feed or lodge poor people there, if necessary. A Beis Medrash is 'Bei (the house of) Rabanan', for they learn there all day. A Beis ha'Keneses is not Bei Rabanan.

Rosh (Bava Basra 1:4): Rav Ashi did not really move his bed into the Beis ha'Keneses. We may not eat or sleep in a Beis ha'Keneses! Rather, he moved in nearby, where guests eat and sleep, like it says in Pesachim.

Me'iri (Sanhedrin 70b DH Seudah): The Yerushalmi says that Seudas Ibur Chodesh was made in the Beis ha'Keneses. One may not eat in a Beis ha'Keneses, i.e. a Seudah of Reshus (not a Mitzvah). The Yerushalmi says that one must check a Beis ha'Keneses for Chametz due to Seudos Ibur Chodesh.

Or Zaru'a (Shabbos Sof Siman 23): R. Nisim Ga'on asked that Shmuel connotes that visitors may eat in a Beis ha'Keneses, but a Beraisa forbids eating in a Beis ha'Keneses! This is even for Batei Kenesiyos of Bavel. We can say that they ate in a house next to the Beis ha'Keneses. I hold that a Tanai permits eating in a different house; Shmuel taught a bigger Chidush, that visiting Chachamim may eat in a Beis ha'Keneses, like Rava taught. Some answer that Seudas Shabbos is a Seudas Mitzvah, so it is permitted in a Beis ha'Keneses, like the Yerushalmi says about Seudas Ibur Shanah.

Beis Mordechai (1:25 DH Teshuvah): The only Heterim to eat in a Beis ha'Keneses are Seudas Mitzvah, and for Chachamim and Talmidim. This is why Tosfos says that they ate in houses nearby. I say that since hosting guests is greater than going early to the Beis Medrash and receiving the Shechinah, and for this one eats the Peros in this world, and the principal is intact for the world to come, it is considered a Seudas Mitzvah, so guests may eat in a Beis ha'Keneses.

Poskim

Shulchan Aruch (OC 151:1): We do not eat or drink in a Beis ha'Keneses or Beis Medrash. Chachamim may eat or drink there b'Dochak

Magen Avraham (2): Also Chachamim must fear the Mikdash! Or Zaru'a permits only in Bavel, because their Batei Kenesiyos are on Tanai.

Mishnah Berurah (5): Similarly, the city may feed or lodge poor people there if necessary. This applies only in Chutz la'Aretz, and some forbid even in Chutz la'Aretz.

Rema: Some permit a Beis Medrash to Chachamim even not b'Dochak.

Mishnah Berurah (9): One who learns all day in a Beis Medrash may rely on the Rema.

Kaf ha'Chayim (12): Some permit visitors to eat even in a Beis ha'Keneses of Eretz Yisrael. The Isur to eat there applies only to residents of the city.

Shulchan Aruch (4): For the needs of a Beis ha'Keneses or another Mitzvah, one may eat and sleep there.

Divrei Yatziv (YD 163:4): In Pesachim (1b) it says they ate on Shabbosos and Rosh Chodesh! Some texts say 'Iburos (Seudas Ibur Shanah) and Rosh Chodesh.'

Magen Avraham (5): Semak permits a Seudas Mitzvah; i.e. like that of Ibur Shanah, which consisted of bread and legumes.

Mishnah Berurah (20): In a meal of bread and legumes, there is no frivolity. He excludes a Seudah with drunkenness; it is forbidden even in a Beis Medrash. We do not protest those who are lenient about a Seudas Siyum ha'Shas, for no other place is big enough; they have whom to rely on.

Sha'ar ha'Tziyon (14): The Ramban and others say that the Tanai in Bavel permits temporary needs of the poor of the Rabim. Some texts of the Yerushalmi permit Seudas Shabbos. Surely this is not only bread and legumes!

Eliyahu Rabah (2): The custom is that when they appoint new leaders in the Beis ha'Keneses, even the ignoramuses eat there. Since it is for needs of the Tzibur, it is as if they stipulated from the beginning. This requires investigation.

Ha'Elef Lecha Shlomo (OC 73): I say that one may not make a wedding meal in the Ezras Nashim. It is less Kodesh than the men's section, but it is still Kodesh. It is improper to eat in one's Master's place!

Har Tzvi (73): The questioner wanted to equate Achilas Arai (not a fixed meal) in a Beis ha'Keneses to Achilas Arai while wearing Tefilin, which is permitted (OC 40:8). The latter pertains to Hesech ha'Da'as (ceasing to think about them), but the former pertains to frivolity. The Tur brings from R. Yonah that Hesech ha'Da'as while wearing Tefilin is due to frivolity. Surely the Isur to eat in a Beis ha'Keneses is even Arai, just like the Isur to sleep. It seems that Tosfos' (Bava Basra 3b DH v'Ailei) text of the Gemara explicitly forbids sleeping Arai (Gra OC 151:3). Minchas Bikurim (on Tosefta Megilah 2:1says that we forbid drinking, which is Arai, and all the more so sleeping Arai. We may likewise learn to Achilas Arai. Perhaps the Isur in a Beis ha'Keneses is due to honor of the Beis ha'Keneses; this is why an individual's eulogy is forbidden. The Rambam connotes like this, but the Shulchan Aruch forbids eating and drinking along with frivolity (Sa'if 1), and discusses honor only in Sa'if 9. I say that it depends on the text in Megilah 28a. Rashi says that the text is 'we do not conduct frivolously. We do not eat, drink...', not 'and we do not eat...' This text forbids eating due to frivolity; the text he rejected disagrees. The text of the Rambam, Tur and Shulchan Aruch is 'and'. The Gra says that this is unlike Rashi.

Har Tzvi: Eating and drinking are essential to life. They are frivolity only due to Kedushas Beis ha'Keneses. The same applies to labor. Rashi (Berachos 23b) says that one removes Tefilin before a fixed meal, lest he get drunik and disgrace the Tefilin. The Magen Avraham (5) permits a Seudas Mitzvah only of bread and legumes. The Pri Megadim explains that this will not lead to intoxication.Such a meal is not intrinsically frivolous, just doing so in a Beis ha'Keneses is frivolous. A Seudas Mitzvah is not frivolous. One may do a Mitzvah in a Kodesh place. The Magen Avraham excludes a Seudas Mitzvah in which there is concern for intoxication. Surely this concern applies to Seudos Shabbos. Or Zaru'a permits Seudos Shabbos. Tosfos and the Ran disagree, therefore, they explained differently regarding Kidush. Perhaps the Ran holds that it is a Seudas Mitzvah on Shabbos, when guests eat from the Tzedakah fund. The Rema (below) connotes that one may not eat Seudas Shabbos in a Beis ha'Keneses.

Rema (366:3): The custom nowadays is to place an Eruv in a Beis ha'Keneses. It is an old custom. This is because our Eruvin are considered Shituf, and it need not be in a house.

Mishnah Berurah (29): Even though a Beis ha'Keneses is not proper to dwell in, due to its Kedushah, for one may eat there only if he learns there, we fulfill the custom because our Eruvin are Shituf.

Sedei Chemed (Asifas Dinim, Beis ha'Keneses 4). People call a Beis ha'Keneses a Beis Medrash, and justify eating and drinking there, (e.g cake and drinks on a Yahrtzeit. I protested.) R. Mordechai Shalom defended them based on the Magen Avraham (568:5), who says that any meal with Chachamim, or with Divrei Torah, is a Seudas Mitzvah. Orchos Chayim (Spinka) says that all Gedolei Yisrael make all Seudos in their Beis Medrash, and one may not suspect that they sin.

Kaf ha'Chayim (151:63): Sedei Chemed (40?) said that surely it is forbidden in a Shul, especially if they serve intoxicating drinks, which always leads to frivolity. See what I wrote in 153:34.

Kaf ha'Chayim (153:34): For a Siyum in a Shul, one may make only a small meal, with only a little wine and no frivolity or idle talk, Chas v'Shalom.

Shevet ha'Levi (9:29): What is the Heter for a Kidush, Seudas Bris or Chasan and Kalah in a Beis ha'Keneses or Beis Medrash? The Mishnah Berurah connotes that the Heter is only in Chutz la'Aretz. The Magen Avraham permits only bread and legumes. Or Zaru'a permits even Seudas Shabbos; it seems this is even in Eretz Yisrael. We learn from the Yerushalmi, which was in Eretz Yisrael. Maharsham (15permits a Seudas Mitzvah in a Beis ha'Keneses or Beis Medrash only if no other place is big enough, but surely not a wedding meal which has frivolity and jesting and women come and go. Divrei Chayim (CM 2:32) says that Chasidic Rebbis are lenient because they never built the place to be a Beis ha'Keneses or Beis Medrash, rather, for a gathering place. We infer that a wedding meal would be forbidden without this. Also Orchos Chayim was lenient because they are not built to have Kedushas Beis ha'Keneses or Beis Medrash. Nowadays they are built for a Beis ha'Keneses or Beis Medrash!

Yechavah Da'as (3:10): Many Poskim permit Seudas Shabbos in a Beis ha'Keneses. This includes Seudah Shelishis, especially if they expound Halachah or Agada. The Ran permits needs of the Rabim. Seudah Shelishis in the Beis ha'Keneses enables the Shi'ur (beforehand) and Minchah to continue until close to sunset, and to begin Seudah Shelishis before sunset and continue the Seudah with words of Torah. Tosfos Rid (Pesachim 101a) says that even in Eretz Yisrael, there was a Tanai to permit guests to eat there. The custom is, on the Yartzite of the elite of the congregation, people learn and make Berachos on food