Gemara

Rav Nachman asked R. Yitzchak to say Divrei Torah during a meal.

(R. Yitzchak): R. Yochanan taught that one may not speak during a meal, lest the food go down the Kaneh (windpipe) instead of the Veshet (foodpipe).

Berachos 43a (Mishnah): If wine was brought during the meal (everyone blesses for himself).

(Beraisa) Question: Why must everyone bless for himself on wine during the meal, but one blesses for everyone on wine after the meal?

Answer (Ben Zoma): During the meal, others are swallowing food when the Mevarech blesses.

Rishonim

Rif (Berachos 31a): Everyone blesses for himself on wine during the meal because others are swallowing food when the Mevarech blesses.

Rashi (Berachos 43a DH Ho'il): During the meal others are swallowing food when the Mevarech blesses, so they will not harken to the blessing.

Rebuttal (Rosh Berachos 6:34): According to this, the Mevarech can be Motzi them if tells them before he is about to bless, so they will finish swallowing first! However, in any case one can have intent while swallowing.

R. Yonah (DH Ba): Some say that we do not want others to answer Amen while food is in their mouths, for this is Mevatel "Yimalei Fi Tehilasecha". This is wrong, for one can say one word properly with food in his mouth.

Rosh and R. Yonah (ibid.): Rather, it is dangerous. The Yerushalmi supports this. It says that similarly, if one sneezes during a meal we do not say 'Asuta' (to prompt the sneezer to pray for his friend, and be healed himself), i.e. due to the danger. Even though people need not say Amen, we are concerned lest they will.

Question: The Mishnah says that one blesses on incense for the others. The Ge'onim say that this is during the meal This is dangerous!

Answer (R. Yonah DH v'Nir'eh): People would be Yotzei without answering Amen. The Yerushalmi asked why incense is different. It answered that everyone smells and benefits from the incense immediately, therefore one blesses for all. If each would bless for himself, some would benefit before blessing. Therefore, it is better that one bless for them, and they are Yotzei without answering. One does not benefit from wine until he drinks, and he will bless beforehand.

Rambam (Hilchos Berachos 4:12): If wine was brought during the meal, everyone blesses for himself. This is because others cannot answer Amen because they are swallowing food.

Rambam (7:6): We do not talk during a meal, lest one be endangered. Therefore, if wine was brought during the meal everyone blesses for himself. If one would bless and another would answer Amen while swallowing, this would be dangerous.

Kesef Mishneh: The Gemara says that one does not bless for the others because they are swallowing food. The Rambam explains that this is due to danger, lest one choke.

Note: Above (4:12) the Kesef Mishneh said that the Bavli forbids because the others are thinking only about swallowing, and the Yerushalmi forbids due to danger.

Poskim

Shulchan Aruch (170:1): One may not speak during a meal, lest the food go down the Kaneh instead of the Veshet. If one sneezes during a meal we do not say 'Asuta'.

Magen Avraham (1): Even Divrei Torah is forbidden during a meal. If Divrei Torah were not said on the table (on which people ate), it is as if they ate from sacrifices to idolatry.

Prishah (1): It seems that one may not talk even between courses, as long as one intends to eat. We learn from the Berachos on wine and ha'Tov veha'Metiv (which are between courses). One may not bless for others unless he prepares them beforehand to finish swallowing (174:8, 175:5). However, perhaps this was only when people used to eat reclining on their left. Then, the Veshet is on top of the Kaneh. When one talks the Kaneh opens and food can fall in, which is dangerous. Nowadays people sit straight while eating, so it is not so dangerous. This is why I do not see people careful about this. However, I did not see anyone make this distinction.

Question (Birkei Yosef 1 and Shiyurei Berachah 1): According to this, when reclining on Seder night we must be careful not to talk while eating. However, even though nowadays we do not recline (167:11), the Shulchan Aruch brings the Isur to talk during the meal! Since people are not careful about this, we cannot do anything about it.

Sha'arei Teshuvah (1): People used to lean on the left to ensure that the food go down the Veshet (Pesachim 108a)! However, we can say that if one talks it is dangerous in any case. Nowadays that many are not careful about this, we need not be careful even at the Seder.

Eshel Avraham (1): Even though we are more stringent about danger than Isur, one may talk to stop a transgression.

Teshuvas Yavi'a Omer (5:OC:16:7, b'Sof): Nowadays that we do not recline, we talk during meals, so all the more so one may answer Amen. However, if he is about to swallow food and it is difficult to answer, it suffices to intend for the proper response, and Shome'a k'Oneh.

Mishnah Berurah (1): The Eliyahu Rabah conlcudes that one may talk between courses. One should say Divrei Torah, at least Mizmor l'David; one should not rely on Birkas ha'Mazon.

Kaf ha'Chayim (157:16): The Zohar says that during a meal one should not speak Divrei Chulin not needed for the meal. One should think Torah, and then the entire meal is like Hakravas Korbanos.

Shulchan Aruch (174:8): If wine was brought during the meal, everyone blesses for himself, even if they reclined to eat together (Rema - because others cannot answer Amen,) for we are concerned lest the food go down the Kaneh instead of the Veshet.

Mishnah Berurah (40,41): Normally, it is better that one bless for everyone, due to "B'Rav Am Hadras Melech". Here it is forbidden due to danger. Even though the others need not answer Amen to be Yotzei, we are concerned lest they will.

Even Divrei Torah is forbidden during a meal. If Divrei Torah were not said on the table (on which people ate), it is as if they ate from sacrifices to idolatry. The SHLaH says that there should be proper Divrei Torah; one should not rely on Birkas ha'Mazon.

Rema: Some say that if the Mevarech says 'Savri Rabosai' and the others listen and intend for the Berachah, cease to eat and answer Amen, one may bless for all of them. This is the custom. 'Savri' means 'intend (to be Yotzei)'; one does not say 'bi'Rshus'.

Taz (11): This opinion holds that one who is swallowing cannot hear the Berachah. Therefore, it helps to say 'Savri', provided that the others cease to eat. The first opinion forbids, lest people continue to eat.

Gra (DH v'Yesh): Tosfos learns from the Yerushalmi (6:6) that 'Savri' helps. R. Yonah and the Rosh (6:32) explain the Yerushalmi differently.

Drishah (4): The Rosh holds that one can hear the Berachah while eating; the concern is danger. Even if one hears 'Savri' he may continue eating, so the danger persists. The lenient opinion holds that one cannot hear the Berachah while eating, so one who hears 'Savri' stops eating, so there is no problem.

Shulchan Aruch (175:5): If different wine was brought and many are eating together, everyone blesses ha'Tov veha'Metiv for himself. One does not bless for all of them, lest the food go down the Kaneh instead of the Veshet when they answer Amen.

Rema: If they were reclining to drink without eating, one blesses for all of them.

Source (Gra DH Aval): We learn from the Mishnah (42a).

Note: Meforshim discuss the Kevi'us of drinking without eating. Seemingly, the reasons why one may not Motzi another in a meal do not apply if they were only drinking. Drinking is not distracting; one can drink and hear and have intent to be Yotzei. It seems that there is no danger, for no normal person even tries to talk before swallowing liquid in his mouth!