Rif Pesachim 27b {Pesachim 120b continues ... 121b; Menachot 65b-66a}

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27b

and eats all that he needs. And then he blesses for each and every one in their houses, and they drink the cup of kiddush and the haggada, and eat matza and vegetables, but he does not eat with them anything at all. And he leaves them to finish their meal, and they bless birkat haMazon, and he goes to another house and does so, and so for each and every house. And at the end he goes to his own house and finishes the Hallel and drinks the cup of Hallel.

And we learn these matters from that which they learnt {in a brayta in Rosh haShana 29a}: All blessings, even though he himself has already fulfilled, he may fulfill for others, except for on bread and blessings on fruits, which if he has not {yet} fulfilled {his own obligation to make a blessing} he may fulfill for others, and if he has fulfilled, he cannot fulfill for others.

And Rechava inquired: The blessing on bread of matza, which is haMotzi, and the blessing of wine for kiddush, which is borei peri haGafen, what {is the law}? {Do we say that} since it is an obligation {=a mitzvah rather than simply a blessing on enjoyment of foods} he fulfills for others, or perhaps it is a blessing {on food} and not an obligation.

And we resolve this from which Rav Ashi said: When we were in the house of Rav Papa, he made kiddush for us, and {later} when his field laborer came in from work, he repeated kiddush for him.

And we derive from this that although he blessed haMotzi for himself on the matza which is an obligation, when there is one who did not hear and did not fulfill his obligation, he repeats the blessing for him, whether it is haMotzi, whether al achilat matza; whether borei peri haAdama, whether al achilat maror; whether borei peri haGafen. All of them are due to one cause -- that they are a commandment.
And so is the halacha.

And he, once he blessed birkat haMazon, he should not taste anything, for we establish that we do not conclude after matza with afikoman.

And if he wishes to put these other houses first, and bless for them, and not eat nor taste anything, and return to his house, the permission is in his hand and it is fine.

Rava said: Matza nowadays is Biblical, and maror is Rabbinic.

Why is maror different in that it is written by it {Bemidbar 9:11}:

יא בַּחֹדֶשׁ הַשֵּׁנִי בְּאַרְבָּעָה עָשָׂר יוֹם, בֵּין הָעַרְבַּיִם--יַעֲשׂוּ אֹתוֹ: עַל-מַצּוֹת וּמְרֹרִים, יֹאכְלֻהוּ.

11 in the second month on the fourteenth day at dusk they shall keep it; they shall eat it with unleavened bread and bitter herbs;

{they shall eat it = the korban Pesach. thus} - at a time when there is a korban Pesach, yes, at the time when there is no korban Pesach, no. In regards to matza as well, it states עַל-מַצּוֹת ?!וּמְרֹרִים יֹאכְלֻהוּ
Regarding matza, Scriptures returns, for it is written {Shemot 12:18}:

יח בָּרִאשֹׁן בְּאַרְבָּעָה עָשָׂר יוֹם לַחֹדֶשׁ, בָּעֶרֶב, תֹּאכְלוּ, מַצֹּת: עַד יוֹם הָאֶחָד וְעֶשְׂרִים, לַחֹדֶשׁ--בָּעָרֶב.

18 In the first month, on the fourteenth day of the month at even, ye shall eat unleavened bread, until the one and twentieth day of the month at even.

{though this is a statement about the entire span of 7 days - however, read the following brayta}

There is a brayta in accordance with Rava: {Devarim 16:8}:

ח שֵׁשֶׁת יָמִים, תֹּאכַל מַצּוֹת; וּבַיּוֹם הַשְּׁבִיעִי, עֲצֶרֶת לַה' אֱלֹקֶיךָ--לֹא תַעֲשֶׂה, מְלָאכָה. {ס}

8 Six days thou shalt eat unleavened bread; and on the seventh day shall be a solemn assembly to the LORD thy God; thou shalt do no work therein. {S}

just as the seventh {mentioned in the pasuk} is voluntary, so are the six days voluntary. What is the reason? This {the seventh, mentioned elsewhere, in Shemot 12:17 as a day in which one eats matzot} is something which was in the general {klal - namely, in Shemot 12:17} and left the general in order to teach - it teaches not just upon itself, but to teach about the entire generality. {And thus matza is something one should eat rather than chametz, but it has the status of reshut rather than obligation to eat.} Perhaps even the first night is voluntary? Therefore it teaches {Bemidbar 9:11} עַל-מַצּוֹת וּמְרֹרִים, יֹאכְלֻהו. I only have {=know} when the Temple is standing {since it is a reference to eating it = the korban Pesach which matzot}. From where do I know when the Temple is not standing. Therefore it teaches {Shemot 12:18}:

יח בָּרִאשֹׁן בְּאַרְבָּעָה עָשָׂר יוֹם לַחֹדֶשׁ, בָּעֶרֶב, תֹּאכְלוּ, מַצֹּת: עַד יוֹם הָאֶחָד וְעֶשְׂרִים, לַחֹדֶשׁ--בָּעָרֶב.

18 In the first month, on the fourteenth day of the month at even, ye shall eat unleavened bread, until the one and twentieth day of the month at even.

Scriptures establishes it as an obligation.

Yerushalmi, in Shevuot, in the third perek: {If he made} an oath not to eat matza, it is forbidden for him to eat matza on the night of Pesach. An oath not to eat matza on the night of Pesach, he is lashed and eats matza on the night of Pesach. An oath that I will not sit in the shade, it is forbidden to sit in the shade of a Succah {on Succot}. An oath that I will not sit in the shade of a Succah, he is lashed and sits in the shade of a Succah.

{So much for oaths regarding matza and Succah. What about wine, in terms of the 4 cups?}

It is written in the Sifrei of the academy of Rav: {Bemidbar 6:3}:

ג מִיַּיִן וְשֵׁכָר יַזִּיר, חֹמֶץ יַיִן וְחֹמֶץ שֵׁכָר לֹא יִשְׁתֶּה; וְכָל-מִשְׁרַת עֲנָבִים לֹא יִשְׁתֶּה, וַעֲנָבִים לַחִים וִיבֵשִׁים לֹא יֹאכֵל.

3 he shall abstain from wine and strong drink: he shall drink no vinegar of wine, or vinegar of strong drink, neither shall he drink any liquor of grapes, nor eat fresh grapes or dried.

to equate wine of a commandment with voluntary wine, etc..

{Pesachim 121b}
Rabbi Simlai visited the house of of people performing a pidyon haBen {redemption of the firstborn}. They asked him: al pidyon haBen, the father certainly blesses. Shehechiyanu, who blesses? Should the cohen bless because the benefit comes to his hand, or should the father of the son blesses because he performs the mitzvah? He did not have {the answer} in his hand. He came and asked in the bet midrash. They told him: The father of the son blesses both.
And the halacha is that the father of the son blesses both.

{Menachot 65b}
And we are obligated to count the days of the seven weeks, from the evening of the 15th of Nissan which is the night of {=beginning} the 16th, for it is written {Vayikra 23:15}:

טו וּסְפַרְתֶּם לָכֶם, מִמָּחֳרַת הַשַּׁבָּת, מִיּוֹם הֲבִיאֲכֶם, אֶת-עֹמֶר הַתְּנוּפָה: שֶׁבַע שַׁבָּתוֹת, תְּמִימֹת תִּהְיֶינָה.

15 And ye shall count unto you from the morrow after the day of rest, from the day that ye brought the sheaf of the waving; seven weeks shall there be complete;

And the Sages learnt {in a brayta}: {Vayikra 23:15}:

טו וּסְפַרְתֶּם לָכֶם, מִמָּחֳרַת הַשַּׁבָּת, מִיּוֹם הֲבִיאֲכֶם, אֶת-עֹמֶר הַתְּנוּפָה: שֶׁבַע שַׁבָּתוֹת, תְּמִימֹת תִּהְיֶינָה.

15 And ye shall count unto you from the morrow after the day of rest, from the day that ye brought the sheaf of the waving; seven weeks shall there be complete;

Each and every person counts for himself.
מִמָּחֳרַת הַשַּׁבָּת - "from the morrow after the day of rest" - from the morrow of Yom Tov {of Pesach}

{Menachot 66a}
And a brayta also says so: {from same pasuk:}

טו וּסְפַרְתֶּם לָכֶם, מִמָּחֳרַת הַשַּׁבָּת, מִיּוֹם הֲבִיאֲכֶם, אֶת-עֹמֶר הַתְּנוּפָה: שֶׁבַע שַׁבָּתוֹת, תְּמִימֹת תִּהְיֶינָה.	15 And ye shall count unto you from the morrow after the day of rest, from the day that ye brought the sheaf of the waving; seven weeks shall there be complete;
טז עַד מִמָּחֳרַת הַשַּׁבָּת הַשְּׁבִיעִת, תִּסְפְּרוּ חֲמִשִּׁים יוֹם; וְהִקְרַבְתֶּם מִנְחָה חֲדָשָׁה, לַיהוָה.	16 even unto the morrow after the seventh week shall ye number fifty days; and ye shall present a new meal-offering unto the LORD.

Perhaps this means that he should reap and bring {as an offering}, and then begin counting whenever he likes? Therefore it teaches {Devarim 16:7}:

ט שִׁבְעָה שָׁבֻעֹת, תִּסְפָּר-לָךְ: מֵהָחֵל חֶרְמֵשׁ, בַּקָּמָה, תָּחֵל לִסְפֹּר, שִׁבְעָה שָׁבֻעוֹת.

9 Seven weeks shalt thou number unto thee; from the time the sickle is first put to the standing corn shalt thou begin to number seven weeks.