Introduction: where this shiur picks up

The Shulchan Aruch, the order of arranging the seder plate on the night of the Seder, se'if 4

"They bring before the master of the house a plate on which there are three matzos, marror, charoses, karpas or another vegetable, vinegar or salt water, and two cooked foods, one in remembrance of the Pesach offering and one in remembrance of the Chagigah offering."
(Shulchan Aruch, se'if 4)

Introduction: where this shiur picks up

What we have covered so far: The main halachos of erev Pesach that falls on Shabbos have already been explained, and only small details remain to round things out.
The point still in front of us: There is a matter that applies specifically to this year, and it does not appear uniformly in all the Haggados (some Haggados bring it and some do not, and each one has its own wording). In order to understand it we first need to look at the halachos of arranging the seder plate, so that is where we are looking now, and we will continue the matter in the next shiur.
The nature of this section: The halachos of the seder plate apply every single year, and in them there is no difference between this year and any other year.

Before whom is the plate placed

"They bring before the master of the house: but before the rest of the members of his household there is no need to set out this arrangement; rather, they all take from that of the master of the house."
(Mishnah Berurah, s.k. 17)

The situation in their times: The master of the house alone arranged the plate, and all the members of the household took from it.
The difficulty in our times: The main difficulty is with the matzos. In earlier generations the matzos were far larger, whereas today a kezayis is half a matzah, three quarters of a matzah, or a third of a matzah, depending on the dispute about the measure of a kezayis and on the type of matzah being used.
Arranging the plate: The one who arranges the plate is the master of the house, and in that respect the halachah is exactly as the Mishnah Berurah says.
Regarding the matzos: Here there are various opinions, because one must eat both from the top matzah and from the middle one, and if the master of the house has to distribute to everyone it can become difficult. For that reason some hold that matzos should be placed in front of each and every person. This matter itself requires its own study and will be explained in its place.

Why we take three matzos

"Three matzos: two for lechem mishneh, as on any other Yom Tov, and one in order to break in two, half of it to fulfill with it the mitzvah of eating matzah, since it is called 'lechem oni' (bread of poverty), and what is the way of a poor man? With a broken piece. And the second half is for the afikoman."
(Mishnah Berurah, s.k. 18)

Two halachos coming together: The first halachah is lechem mishneh (two loaves), which according to some poskim applies on Yom Tov as well. The second halachah is that the matzah of the mitzvah, the one we eat at the Seder and over which we recite "al achilas matzah," must fit the definition of lechem oni.
The view of the Gra: There is an opinion that one takes only two matzos, and that is the view of the Gra and others. According to this view, since at the Seder we must have a broken piece, lechem mishneh here is reduced in status, and one takes a whole matzah and a half.
The parallel to this year's constraints: Just as this year, when erev Pesach falls on Shabbos, we forgo bread at seudah shlishis even though every other year we eat bread at it, so too there are constraints here, and according to this view lechem mishneh gives way before the need for a broken piece.

Three explanations of "lechem oni"

Flour and water alone: Lechem oni means that it contains nothing but flour and water, as opposed to matzah ashirah ("rich matzah"), into which one puts oil, wine and the like.
That many things are recited over it: The matzos lie on the table and we recite the Haggadah over them. That is why the matzos are uncovered throughout the Haggadah, while at the moments when the wine takes center stage we cover them: at Kiddush, and likewise at "Vehi she'amdah" when we hold up the cup.
The way of a poor man is with a broken piece: A poor man cannot afford to buy a whole loaf, so he eats broken pieces, halves and quarters of loaves.

(All three explanations are the words of the Gemara in explaining "lechem oni" as it appears in the Torah.)

From here to the order of Yachatz, Motzi and Matzah

Yachatz: Since the matzah of the mitzvah must be broken and not whole, its definition being lechem oni, we break the middle matzah in two: the larger piece for the afikoman and the smaller piece for the matzah of the mitzvah. That is why the order is Yachatz and only afterwards Maggid.
The berachah of Hamotzi: The berachah "Hamotzi lechem min ha'aretz" must be recited over a whole loaf, and not over one matzah alone but over lechem mishneh. Therefore one holds the entire bundle: a whole matzah on top and a whole matzah on the bottom, with the broken piece in the middle.
After the berachah: He puts down the bottom matzah and holds the top one together with the broken middle one, and over those he recites "al achilas matzah."
Why we eat from both: On the one hand a whole matzah is needed for lechem mishneh, and on the other hand he must eat a broken piece for lechem oni, so we cut from both. If he does not eat from the top one, it turns out that he has not eaten from lechem mishneh, since lechem mishneh is the whole matzah on top together with the whole one on the bottom. We eat a kezayis from this one and a kezayis from that one, which comes to two kezaysim.

(There are additional approaches to this matter, and what has been presented here is the simplest of the explanations.)

Contrasts at the Seder

Eating lechem oni while reclining

The difficulty: If the matzah is lechem oni, why do we eat it reclining, which is the manner of freedom?
The explanation: These are two separate things. The food itself must be lechem oni, while the manner of eating conveys that we have become free men. At the Seder we create many contrasts, and this is one of them.

Further contrasts

The text of the Haggadah: "We were slaves" set against going out to freedom.
The first two cups: From the words of the Gemara there is room to say that those should have been drunk without reclining, and we drink all of them reclining because of the doubt.
The charoses: The Gemara says explicitly that we put bitter items into the charoses, meaning the clay-like texture and the wine, which recall the servitude, and into that very mixture we put good items: apple and the fruits to which the Jewish people are compared, which recall the redemption, based on the verse "under the apple tree I awakened you." So the charoses itself is made up of two opposites.
Korech: There is a question whether it is eaten reclining or not reclining, since from the standpoint of the matzah in it reclining is required, while from the standpoint of the marror in it there is no reclining. This too is one of the contrasts.

Charoses

"Charoses: in order to dip the marror in it, as explained further on."
(Mishnah Berurah, s.k. 19)

Mitzvah or optional: There is no mitzvah to eat charoses, and there is also no prohibition against eating it, and there are people who do eat some of it.
Its primary function: To dip the marror in it.

Karpas: identifying the vegetable

"Karpas: it is a type of vegetable that is called karpas."
(Mishnah Berurah, s.k. 19)

A precise reading of the Mishnah Berurah: When it says "karpas" the intent is a particular vegetable whose name is karpas. Just as it says marror and we take marror, it says egg and we take an egg, it says shankbone and we take a shankbone, so too it says karpas and seemingly one should take karpas, whereas nowadays we take a potato, which is not karpas.
The difficulty outside Eretz Yisrael: Outside Eretz Yisrael karpas was not available, and people did not even know what it was.
The view of most researchers: Karpas is celery or parsley.
The problem with parsley: Most people do not eat it as it is; they use it in soup or chop a little of it into a salad, and although there are those who eat the leaves as they are, that is a minority.
The rule of berachos in such a case: A vegetable that most people eat cooked, if one eats it raw he is not eating it in the usual manner and he recites shehakol over it. So it is with a raw potato: one who eats it recites shehakol, because most people eat it cooked.
The practical conclusion: If he takes parsley for karpas he has gained nothing, since most people would recite shehakol over it and we need borei pri ha'adamah; and the same applies to celery, which carries the very same doubt. Therefore we take a potato, or any vegetable whose berachah is certainly borei pri ha'adamah: kohlrabi, radish, carrot or scallion, whatever one has available.

The reason for karpas and the dipping

So that the children will ask: The Gemara says that the dipping is done so that the children will ask, and that is "why is this night different, that we dip," and this dipping is the answer to the question.
Why specifically a vegetable: For the sake of prompting the question alone one could have dipped anything, even meat in salt. Rather, there is a halachic reason here.
The doubt about the berachah on marror: Marror is a vegetable, and seemingly it requires the berachah of borei pri ha'adamah; but not everyone derives pleasure from it, somewhat like the rule that we do not recite a berachah over medicine. The poskim therefore disagree whether one recites borei pri ha'adamah over the marror or not.
The solution provided by karpas: To get out of the doubt, the poskim instituted eating karpas, provided that it is a vegetable whose berachah is certainly borei pri ha'adamah, and when he recites the berachah over it he should have the marror in mind as well. That is why they were careful not to dip meat or anything else in salt water, but specifically a vegetable.
The difficulty with this solution: From karpas until marror roughly two hours generally pass, and nevertheless the poskim were lenient about this, as they have no alternative. This is one of several places at the Seder where the poskim are lenient in matters of berachos because of the flow of the Seder, while in other instances they are strict and are not lenient.

In passing · Birchos hanehenin at the Seder and in general

1. A berachah over medicine

The rule: One who takes medicine does not recite a berachah over it, because it has no good taste and he derives no pleasure from it.
One who swallows without chewing: Someone who swallows and receives no taste has no pleasure that would obligate a berachah.
One who chews the medicine: He too does not recite a berachah, since it is medicine and has no good taste, and this is not the pleasure of eating.

2. The berachos on wine for the cups of the Seder

The opening berachah: Ashkenazim recite borei pri hagafen over each and every one of the four cups.
The concluding berachah: Over the first two cups one does not recite a separate concluding berachah, since the Birchas Hamazon recited afterwards covers the wine. And the concluding berachah at the end of the Seder is not covering the first cup.
The character of the meal: The Seder meal is a complex one; we interrupt it with speech and perform various acts in the middle of it, and because of that several problems in berachos arise in it, and for each one the poskim found its own resolution.

(In closing it was hinted that the letter samech in the word "karpas" stands for "sof," the end, and the continuation will be explained in the next shiur with Hashem's help.)