Bedikah and biur chametz when erev Pesach is Shabbos

Shulchan Aruch, Siman 444: the laws of erev Pesach that falls on Shabbos, containing eight se'ifim
"When the fourteenth of Nisan falls on Shabbos, we perform the bedikah (the search for chametz) on the night of the thirteenth, and we destroy everything before Shabbos, leaving over food for two seudos for the needs of Shabbos. The time for the third seudah is after Minchah, and at that point one can make it neither with matzah nor with chametz, but only with matzah ashirah, and it must be eaten before the tenth hour."
(Shulchan Aruch, se'if 1)

(This siman applies in practice only rarely; by the calendar reckoning, the next time erev Pesach will fall on Shabbos is about twenty years from now.)

Bedikah and biur chametz when erev Pesach is Shabbos

1. Moving the bedikah up to the night of the thirteenth

The usual time and the change: The bedikah was established to be done by candlelight on the night of the fourteenth. But when the night of the fourteenth is Friday night, we do not search then, so the bedikah is moved up to the night of the thirteenth, that is, Thursday night.
Searching on Friday night by electric light: In principle one could search by electric light, but this is not desirable and it is not the preferred way, and that is why the Chachamim moved the bedikah earlier.
Why not Friday morning: We do not search by sunlight, and even candlelight during the day does not allow for a proper bedikah. This whole arrangement is the ideal practice.

"And one must recite the berachah over the bedikah."
(Mishnah Berurah, s.k. 1)

Berachah and bittul: Although when a bedikah is done outside its regular time there is a discussion whether a berachah is recited, here this is the time set for the bedikah in such a year, so a berachah is recited, and bittul (nullifying the chametz) is also done just as in any other year.

"Because tomorrow, on Friday, it is impossible to search, since we do not search by sunlight."
(Mishnah Berurah)

2. Destroying the chametz and leaving food for two seudos

When the chametz is burned: One who searched on the night of the thirteenth burns the chametz the next morning, on Friday, destroying everything before Shabbos.
The meaning of "food for two seudos": This refers to the minimum amount of chametz that must be left over for the needs of Shabbos, the Friday night seudah and the Shabbos morning seudah, since on Shabbos one needs lechem mishneh (two loaves) and must eat bread. On Friday itself there is no limit on how much one may eat, but at the onset of Shabbos he must have these two seudos on hand.
Guarding the chametz on Shabbos: The Mishnah Berurah cautions that the chametz that was left over should be placed in a tucked-away spot.

3. The Shabbos morning seudah

Rising early for davening: Chametz may be eaten until the end of the fourth hour, which according to the calendars is roughly ten o'clock (some calculate ten thirty), so one rises early to daven.
Not to prolong the davening: The Mishnah Berurah stresses that the davening should not be drawn out at length, so that there will be time to eat the second seudah with chametz, and so that people not stumble into eating chametz after its permitted time.

The third seudah: neither with chametz nor with matzah

The problem: The time for the third seudah is after midday, and according to many opinions after davening Minchah. At that hour there is no longer any possibility of eating chametz, since its time ended at the tenth hour of the reckoning that was established, and on the other hand matzah too is forbidden.

"Not with matzah - because it is forbidden to eat matzah on erev Pesach."
(Mishnah Berurah, s.k. 5)

"Anyone who eats matzah on erev Pesach is like one who is intimate with his arusah (betrothed) while still in his father-in-law's house."
(Chazal)

Explaining the comparison: The arusah is already betrothed to him and is considered his wife, as is implied by the berachah of eirusin, and nevertheless he may not live with her until he marries her under the chuppah. So too with matzah: only a few hours remain until it becomes permitted and becomes a mitzvah, and one does not rush to eat it before its time.
The conclusion for such a year: On a Shabbos that is erev Pesach, matzah is forbidden from the morning (from alos hashachar or from sunrise), even though chametz bread is permitted until the end of the fourth hour.

The types of matzah and their definitions

Matzas mitzvah (in one sense): Matzah baked on erev Pesach. In a year when erev Pesach falls on Shabbos there is no possibility of baking on erev Pesach, so there is no such matzah.
Matzas mitzvah (in a second sense): The matzah with which one fulfills the mitzvah at the Seder, over which one recites "asher kideshanu bemitzvosav vetzivanu al achilas matzah" in addition to the berachah of Hamotzi. The name is shared by both senses, and that is the source of the confusion: the essential point is that it is the matzah with which the mitzvah is fulfilled at the Seder, not the fact of having been baked on erev Pesach.
Matzah aniyah: This is the "lechem oni" of the Torah, the matzah with which one fulfills the obligation at the Seder.
Matzah ashirah: As will be explained below, dough kneaded with fruit juice rather than with water.
Additional types: There is also matzah shemurah, ordinary matzah, and matzah sheruyah (soaked matzah), and their definitions will be explained in their proper places.

Three explanations of "lechem oni"

From flour and water alone: The simple and widespread explanation: it contains no leavening agents and no additives whatsoever, and it is therefore the bread of poverty.
Bread over which things are recited: The matzah lies on the table while the Haggadah is read, and the word "oni" is understood from the root meaning to respond or to declare.
A further explanation: Brought in the Gemara, and it will be explained elsewhere.

Matzah ashirah: definition and dispute

"But only with matzah ashirah - meaning that it was kneaded with fruit juice alone."
(Mishnah Berurah, s.k. 6)

The definition: Matzah ashirah is the opposite of lechem oni. It is not flour and water, but flour kneaded with fruit juice alone, such as orange juice, grapefruit juice, wine or eggs, producing a richer and tastier baked product.
The Shulchan Aruch's position: Since it is not chametz and it is not the matzah with which the mitzvah is fulfilled, one may use it for the third seudah on a Shabbos that is erev Pesach.

The rule of eighteen minutes

Flour and water: According to the accepted halachah, flour and water at room temperature do not become chametz in less than eighteen minutes, and if they were placed in the oven and baked within that time, the baking halts the chemical process.
After the baking: Matzah that was properly baked can never become chametz again, even if one cooks it, fries it, grinds it into matzah meal and soaks it in water. This rule is also relevant to the laws of matzah sheruyah.
Fruit juice: This time limit was established for flour and water only. For fruit juice no time for becoming chametz was established, and it is not known whether it is ten minutes, seven minutes or something else, since each substance may behave differently.

The Rema and the Ashkenazi custom

"And in these lands, where the custom is not to eat matzah ashirah..."
(the Rema)

The solution collapses: According to Ashkenazi custom, matzah ashirah is not eaten at all, and therefore the Shulchan Aruch's advice to use it for the third seudah is not applicable to them.
The first reason: It is very difficult to obtain fruit juice that is entirely free of any admixture of water, and there is reason to be concerned that a drop of water got mixed in, in which case we are once again dealing with flour and water.
The second reason: Even if the fruit juice is entirely pure, the time it takes to become chametz together with flour is unknown, and it is possible that it becomes chametz in less than eighteen minutes.
The stringent conclusion: According to Ashkenazi custom, matzah ashirah is not merely "not matzah"; from their perspective it is treated as chametz, and that is the core of the difficulty.
The Sephardi position: Completely pure fruit juice together with flour does not come to become chametz, or else its status is the same as flour and water with the eighteen minutes, so there is no room for concern. The claim that almost every substance in nature contains water is not decisive, because orange juice is defined as orange juice and not as water.
A practical note: It was raised that the factories do not manufacture matzah ashirah in this manner, and this presents a practical difficulty.

The berachah on matzah ashirah and the order of the alternatives

The dispute about the berachah: Some say its berachah is "borei minei mezonos," and some say one recites "Hamotzi lechem min ha'aretz" over it.
The consideration of the seudah: Even if its berachah is mezonos, it is still the preferred way to have the third seudah. The order of preference is this: if one cannot have a seudah with Hamotzi, he goes down to the level of mezonos, and if he has no mezonos he fulfills it with fruit, with the berachah of shehakol.
The question on the Sephardi position: If according to the Sephardim matzah ashirah can serve as matzah, and at the Seder one recites Hamotzi over it because the mitzvah raises it in status, then seemingly this is the very same matzah that may not be eaten on erev Pesach.
The basis for permitting it: The prohibition of eating matzah on erev Pesach was stated regarding lechem oni, the matzah with which one fulfills the mitzvah at the Seder, so that one should feel its distinctive taste that night.

From when does one refrain from matzah, and from which matzah

From the beginning of erev Pesach or from the morning: Some said the prohibition begins from the morning of the fourteenth, and some said that erev Pesach begins from the night before, and according to them, in such a year the prohibition applies already from Friday night. There is no single, decided ruling here.
Customs of refraining earlier: Some do not eat matzah already from Rosh Chodesh Nisan, and those who are more stringent refrain from thirty days before Pesach.
Matzah ashirah during the year: According to Ashkenazi custom there is no objection to buying and eating matzah ashirah until the time when chametz becomes forbidden, since it is not the matzah with which the mitzvah is fulfilled at the Seder, and eating it does not detract from the Seder. Once the time when chametz becomes forbidden arrives, it may no longer be eaten.
Matzah ashirah on a Shabbos that is erev Pesach: On Friday night there is no problem with it. In the morning, apart from the question of chametz, there are Ashkenazim who are stringent not to eat matzah ashirah already from the morning because it resembles matzah, and on this there is a dispute.

In passing · Reciting Shir HaShirim at the Seder

The custom: There is a custom to recite Shir HaShirim at the Seder after finishing the Haggadah.
Its connection to Pesach: Shir HaShirim is the book of Pesach, and in it we read, "leaping over the mountains, skipping over the hills."
The comparison to the night of Shavuos: It was raised that comments about the difficulty of staying awake are not a valid objection, and that in this regard it carries even more importance than the tikkun of the night of Shavuos.