Yachatz is not mentioned in the Gemara. What is the foundation for yachatz? There is a halachah of chotfin matzah on the night of Pesach, simply to steal matzah one from the next to stimulate the curiosity of the children to ask. Rambam’s formulation is the basis for the custom to hide/steal the afikomen. But why do we break it? The Gemara says we emulate a poor person whose daily meal consists of scraps of bread, perusah. We therefore take a complete matzah and break it. The Yerushalmi compares matzah to the relationship between a bride and groom. According to the Vilna Gaon, we have seven blessing on Pesach night just like we have seven blessings at a wedding or Sheva Brachot. (Borei Pri Hagefen, Kiddush, Shehecheyanu, Borei Pri Ha’adama, Asher Ge’alanu, Al Achilas Maror, Hamotzi and Al Achilas Matzah.)
Ha lachma anya is the only Aramaic section in the Haggadah, it is of unknown authorship. Some say it came after the Churban. As the Paschal lamb required a group, and there was no longer a sacrifice to unite the group, announcing to others to come and join in the Seder was a way to maintain the group concept. Simchat haregel is connected with chesed, tzedakah. When the Torah speaks about rejoicing before Hashem, it always includes the obligation to gladden the poor and widow as well. On Yom Tov we don’t give tzedakah but we must demonstrate that we are not stingy. Rambam says that one who does not give charity or does not invite the poor, widows, orphans, transforms the joy of the festival into gluttony. He does not fulfill the obligation of simchas Yom Tov. Chazal say that the ahavat Yisrael demonstrated among the Jews on the night of the Exodus was a major merit for the redemption. We emulate that on Pesach night.
The second cup of wine is associated with the four questions. Rambam says that we fill the second cup of wine and here the child asks and says, kan haben sho’el va’omer. What is added by the word va’omer? Rambam says it refers to the Seder leader who is reciting the Haggadah, that the Exodus story must be said in question and answer format and the questions must be reviewed by the leader. Many families have the custom that everyone at the Seder recites the four questions, not just the individual son.
We start with genus and end with shevach with Avadim Hayinu, ostensibly in response to the child’s questions and continue with the stories of Rabbi Eliezer Ben Azaryah, and the great scholars in Bnei Brak. What is the connection to the questions that were asked? These are all prefaces to the actual answer. First we start with the laws of the evening, that even great scholars must fulfill sippur yetziyat Mitzrayim. Then we say we must teach and answer each child according to capacity. We describe the particulars of the mitzvah we are performing, and express faith in Hashem to fulfill His promise to protect us. We then continue to expound on Arami oved avi, which details the answer and events we are commemorating.
Why use Bikurim, from Dvarim, instead of the actual Exodus story from Shemos? Why use a section where each phrase was supported with a verse from the Exodus story anyway? Chazal felt that over time, people who were many generations removed from the Exodus, secure in their land, under their vineyards and fig trees, would eventually lose appreciation of the actual Exodus story. Therefore, the section of giving thanks for the abundance Hashem gave them, as described in parshat Bikurim, would cause them to fully appreciate the Exodus event that brought them to that point.