By when must one eat the Matzah [of Motzi Matzah] on the night of the Seder?[1]
One is required to fulfill the Mitzvah of eating Matzah prior to midnight.[2] [If one eats the Matzah only after midnight, some Poskim[3] rule he does not fulfill his obligation and has thus lost the Mitzvah. Other Poskim[4] rule he can nevertheless fulfill the Biblical Mitzvah up until Alos Hashachar. Other Poskim[5] rule that this matter is left in question, and hence one is to be stringent like both opinions, and eat Matzah without a blessing. Practically, if one did not yet eat the Matzah and it is already after midnight, he is to eat the Matzah without the blessing of “Al Achilas Matzah.”[6] If it is already close to midnight and one did not yet eat the Matzah, he is to skip from wherever he is holding and perform Motzi Matzah before midnight. The same applies to a person who awoke from a sleep moments before midnight that he should say Kadesh and immediately afterwards recite Motzi Matzah.[7] This applies for both the first and second Seder.[8]]

Until how late may one begin the Seder-May one delay eating Matzas Mitzvah [of Motzi Matzah] until past midnight?[9]   
No. One who does so enters into a question as to whether he has forfeited the Mitzvah, and hence is to eat Matzah without a blessing. Thus, those who desire to begin their Seder after the Mivtzaim Seder, must beware to at the very least eat the Matzah before midnight.

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[1] Admur 458/2 “One is required to eat the Matzah prior to midnight, just like the law regarding the Karban Pesach which may only be eaten until midnight,”; Admur 639/20 “And one is to beware to eat in the Sukkah prior to midnight, just as is required regarding eating Matzah”; 477/6 regarding Afikoman; See 472/2 regarding the Hekesh being used to obligate eating Matzah after Tzeis Hakochavim [Vetzaruch Iyun why the end time was not mentioned in this Hekesh, and why we make the Hekesh for the end time only regarding Matzah and not the four cups, also Tzaruch Iyun why in 475/20-23 no mention of Chatzos was made; See here: http://shulchanharav.com/text.asp?index=128712&arc_id=138425]; Michaber 477/1 and Beis Yosef 477 regarding Afikoman;  Degul Merivava 477; Shaareiy Teshuvah 477/1; M”B 477/6 “One must be very careful”; Biur Halacha 477; Kaf Hachaim 477; Piskeiy Teshuvos

[2] The reason: As just like the Karban Pesach may only be eaten until midnight, so too the Matzah may only be eaten until midnight, as the verse states Al Matzos Umerorim Yochluhu, thus teaching us that the eating of Matzah is connected, and follows similar laws, to the Pesach [Admur 458/2] This follows the opinion of Rebbe Elazar Ben Azaria, brought next.

[3] Reb Elazar Ben Azaria in Pesachim 120b; Zevachim 57b; Tosafus Zevachim ibid; Megillah 21a; Piskeiy Tosafus Pesachim 334; Zevhacim 33; Rabbeinu Chananel in Arvei Pesachim; Semag in name of Riy; Mordechai end of Pesachim; Rabbeinu Yerucham 5/4; Conclusion of Or Zarua; Hapardes 9/16-26 “It is forbidden to eat Matzah after midnight”; See Biur Halacha 477/1 “Viyihei Zahir”

[4] Rebbe Akiva in Pesachim and Zevachim ibid; Rambam Karban Pesach 8/15; Chametz Umatzah 6; Rif [brought in Mishkanos Yaakov 139] Rav Hamaggid; Baal Haitur; Or Zarua in name of Rav Yaakov of Krubil; Kol Bo 90; See Biur Halacha 477/1 “Viyihei Zahir”

[5] Rosh; Rashba; Ran end of Megillah chapter 2; Rokeiach

[6] Degul Merivava 477; Shaareiy Teshuvah 477/1; P”M 477 M”Z 1; Derech Hachaim; Tov Ayin 38/87; Ikarei Hadat 19/14; Misgeres Hashulchan 119/11; Aruch Hashulchan 477/5; M”B 477/6; Biur Halacha ibid; Kaf Hachaim 473/16; 475/64; Beis Halevi 1/34; Nitei Gavriel 91/1

Other opinions: Some Poskim rule that the final ruling of the Talmud is like Rebbe Akiva that the Mitzvah of Matzah applies throughout the night, until Alos Hashachar. [Mishkanos Yaakov 139; Or Yisrael 475; Or Sameiach 6/1; Sdei Chemed Mareches Chametz Umatzah 14/11; See Nitei Gavriel ibid footnote 1]

[7] Degul Merivava 477; Shaareiy Teshuvah ibid; M”B 477/6; Ashel Avraham Butchach 477; Kaf Hachaim 477/10

[8] Admur 481/1 “There is no difference between the first and second night in any other matter”; Nitei Gavriel 91/5

Other opinions: Some Poskim defend the practice of those who recite a blessing over the Matzah even after midday. [Darkei Chaim Veshalom 605; See Nitei Gavriel ibid footnote 6]

[9] See Halacha ?? where this matter was discussed in detail