Gemara

(Beraisa): On that day, R. Akiva expounded that when Yisrael came ashore from the Yam Suf, they decided to sing. Moshe and Yisrael sang like an adult leading the Tzibur in Hallel. They answer the start of the Perek;

Moshe sang "I will sing to Hash-m." They answered "I will sing to Hash-m." Moshe sang "for He is greatly exalted." They said "I will sing to Hash-m."

R. Eliezer the son of R. Yosi ha'Glili says, they sang like a minor (who cannot be Motzi adults) leading the Tzibur in Hallel. They repeat everything that he says:

Moshe sang "I will sing to Hash-m." They answered "I will sing to Hash-m." Moshe sang "for He is greatly exalted." They said "for He is greatly exalted."

R. Nechemyah says, they sang like a teacher leading the Tzibur in the Berachos of Shema Yisrael. He begins, and they continue.

R. Akiva expounds "(Moshe sang and Bnei Yisrael...and they said) saying" - they kept saying the first thing that Moshe said. R. Eliezer says, "saying" refers to everything Moshe said. R. Nechemyah expounds "and they said" to teach that they all said together. "Saying" teaches that Moshe began for them.

38b (Rava): Our custom of Hallel is that the Shali'ach Tzibur says "Baruch ha'Ba", and the Tzibur answers "b'Shem Hash-m". This teaches that Shome'a k'Oneh.

Rishonim

Rif and Rosh (Sukah 19b and 3:28): If one heard but did not answer, he was Yotzei.

Rambam (Hilchos Berachos 1:11): If one heard an entire Berachah and intended to be Yotzei, he was Yotzei even if he did not answer Amen. If one answers Amen to a Berachah it is as if he blessed himself, if the Mevarech (the one who blessed) was obligated to make the Berachah. If mid'Oraisa one must bless, he can be Yotzei by listening only if the Mevarech was also obligated mid'Oraisa.

Rosh (Pesachim 1:10): The Riva says that if a Mitzvah can be done through a Shali'ach, we bless "Al Mitzvas..." If not, not we bless 'Le...', e.g. 'Likro Es ha'Hallel.' Even though Shome'a k'Oneh, like regarding Megilah, it is a Mitzvah to answer the beginning of each Perek.

Ran (Megilah 13b DH Aval): Rashi says that Pores Al Shma is to say Kaddish, Borechu, and the first Berachah before Kri'as Shma. The Ge'onim explain that it is for a Shali'ach Tzibur to begin the Berachos of Shma to be Motzi others. This is unlike other Berachos such as Kidush and Havdalah, in which Reuven can be Motzi Shimon whether or not Shimon answers Amen. The general rule is Shome'a k'Oneh, except for Berachos for Hana'ah.

Hagahos Ashri (Rosh Hashanah, Sof Perek 3): Reuven can be Motzi Shimon in Birkas ha'Mitzvos even if Reuven is not doing the Mitzvah, except for Birkas ha'Mazon, Kri'as Shma and Tefilah. In these he can be Motzi only if he himself is Yotzei now.

Poskim

Shulchan Aruch (OC 6:4): Some people have the custom that one person says Birchos ha'Shachar and the others answer, then one of them says them and the rest answer... This is not a problem of unnecessary Berachos, for the one blessing does not intend to be Motzi them, and even if he did, they do not intend to be Yotzei.

Mishnah Berurah (13): The Levush says that without a Minyan one cannot Motzi another even if they intend. The Pri Megadim says that the Levush agrees that one who is not Baki is Yotzei without a Minyan.

Rema (59:4): In Birchos Kri'as Shma the Shali'ach Tzibur is Motzi an individual even if he is Baki. However, this is only with a Minyan.

Beis Yosef (69 DH Tanan, citing R. Yonah): Regarding Shemoneh Esre, the Shali'ach Tzibur is Motzi people in the fields who are unable to come to the Beis ha'Keneses. Regarding Shma they must say it or be Yotzei by answering Amen amidst a Minyan. This is why Pores Al Shma requires a Minyan. Without 10, answering Amen does not help

Beis Yosef (DH Kosav Adoni Avi): The Rosh was afraid to be Yotzei Birchos Kri'as Shma by listening to the Shali'ach Tzibur, for if his Kavanah lapsed while listening he was not Yotzei. One who says a Berachah himself is Yotzei even if he had a lapse of Kavanah. On Rosh Hashanah and Yom Kipur R. Yonah said the entire Berachah except for the closing, for which he was Yotzei through the Shali'ach Tzibur. He was confident that he would not have a lapse of Kavanah. Alternatively, the Berachos of Rosh Hashanah and Yom Kipur are different, for then a Shali'ach Tzibur is Motzi the Rabim. Even though we learned that a Shali'ach Tzibur is not Motzi a Baki in the city, this is only regarding Shemoneh Esre, which is a request for mercy.

Magen Avraham (5): All agree that one who is not Baki is Yotzei even without a Minyan by listening to Berachos, except for Shemoneh Esre.

Mishnah Berurah (21,23): Except for Berachos over Hana'ah, Reuven can be Motzi Shimon, even if Reuven was already Yotzei and Shimon is a Baki. A Minyan is required only for Birchos Kri'as Shma, and Birchos ha'Shachar according to the Levush.

Mizrachi (Teshuvah 42): One can be Yotzei Shma by hearing it.

Rebuttal (Maharam Alashkar, cited in Pri Chodosh 62:1): This is wrong. The Mitzvah is Kri'ah, not to hear it. The Ritva says that in Shma and Tefilah a Baki is not Yotzei through hearing.

Defense (Pri Chodosh, ibid.): The general rule is, Shome'a k'Oneh. The Ritva clearly holds that one who is not Baki can be Yotzei through hearing! The Yerushalmi says that everyone should himself say Shma, Birkas ha'Mazon and Shemoneh Esre. The reason for Shma is to fulfill "V'Shinantam" himself, not because Shome'a k'Oneh does not apply. Also regarding Shemoneh Esre and Birkas ha'Mazon, a Baki can be Motzi an ignoramus. Regarding Yetzi'as Miztrayim and other matters about which it says 'Zechirah', one is Yotzei through hearing. We learn Megilah from a Gezeirah Shavah 'Zechirah- Zechirah', and one is Yotzei through hearing.

Shulchan Aruch (689:10): Where there is not a Minyan, if only one knows how to read the Megilah, he exempts everyone. If all know, everyone reads for himself.

Magen Avraham (10): We must say that Kri'as ha'Megilah is like Tefilah, in which one needs a Minyan to be Motzi others. Some say that one may bless for everyone even without a Minyan, even if they are Baki. If so, it is better to do so because of "B'Rav Am Hadras Melech".