Why did Hashem refer to Yisrael as his firstborn son?
Rashi #1: "Bechori" means (not firstborn but) great (important). 1
Rashi #2: Hashem was substantiating that Eisav's sale of the birthright to Ya'akov was valid.
Seforno: Because they have a place of honor with Hashem, since they were the first to worship Him. 2
However this does seem to go well with the following Pasuk.
Seforno: Even though He expects all nations to call His Name (See Tzefanyah, 3:9). In a similar vein, the Meshech Chochmah explains that, just as a Bechor gives his father the status of a father, so too, were Yisrael the first to acknowledge Hashem and to give Him the status of Master of the world.
Why does the Torah insert "Hashem Elokav"?
Ramban: To remind the king that, although he is the master who need be afraid of nobody, he is obligated to fear Hashem who is Master over the masters. 1
Rosh (1:3): There is no one to demand [that he atone for] his sin. Therefore, no one else offers his Korban (a male goat for a Chatas).
Da'as Zekenim (23, citing Bechor Shor): If only Hashem knows for sure that "v'Ashem", he brings Asham Taluy. When he finds out (the next verse - "Oh Hoda Elav"), he brings a Chatas. Toras Kohanim supports this.
What are the implications of "v'Ashem"?
Ramban, Moshav Zekenim (23): It implies that he sins and is subject to punishments. The next verse adds "Oh Hoda Elav Chataso" - if he brings a Korban and atones, he avoids punishment.
Seforno #1: It implies that he himself is aware that he sinned. 1
Seforno #2 (on Pasuk 27): It implies that he is obligated to do Teshuvah before bringing his Korban. 2
Moshav Zekenim: This implies Mezid. The Torah begins with Shogeg and ends with Mezid, to teach that even if he was Shogeg, he is considered Mezid, for he causes others to sin after him.
Why is Chatas Nasi written right after Chatas ha'Kahal?
Moshav Zekenim This teaches that one who is able to protest, and does not, the Torah considers it as if he sinned.