What was his jealousy for Hashem, and how does this explain why he is here?
Radak: He killed Nevi'ei ha'Ba'al who caused Yisrael to stray. This caused him to [need to] flee Izevel.
Mesilas Yesharim (Perek 19): Kin'as Hashem is hatred of those who hate Him, and striving to subdue them as much as he can, so Avodas Hashem will be done and His honor will be increased.
Malbim: I killed Nevi'ei ha'Ba'al, and due to this they seek to kill me. I cannot be a Navi to instruct and rebuke this nation!
What Bris does he refer to?
Radak: It is the Bris You made with them on Har Sinai.
Radak citing Pirkei d'R. Eliezer 29: They nullified Bris Milah.
Which Mizbechos does he refer to?
Rashi: It is individual's Bamos that were l'Shem Shamayim 1 . The Mizbe'ach of the Beis ha'Mikdash was in Yehudah (outside of Achav's jurisdiction).
Radak: This is "Mizbach Hashem he'Harus", i.e. the Mizbe'ach that Sha'ul built in Har ha'Karmel.
Was Eliyahu the last Navi Hashem? Ovadyah hid 100 Nevi'im in caves!
Radak: Since they were not known, it is as if they were not.
QUESTIONS ON RASHI
Rashi writes that they destroyed individual's Bamos that were l'Shem Shamayim. Why did Eliyahu complain about this? Once the Beis ha'Mikdash was built, it was forbidden to offer on Bamos!
Har Tzvi Nezikin (Avodah Zarah 52b:3): R. Yisrael Reizman said that even though Bamos became forbidden, they kept their Kedushah and it was forbidden to destroy them 1 , like the Chasam Sofer (OC 32 says). I say that perhaps the Chasam Sofer discusses only Bamas Tzibur. Chashukei Chemed (Eruvin 2a) - his words imply even an individual's Bamah. Zecher Yitzchak (Kunteres Acharon 2) - Chizkiyah correctly decided to eradicate the Bamos and Mizbechos (Avos d'R. Nasan 2). This shows that there was a reason to forbid!