Why did Hashem add "asher Egypt Ma'avidim osam" here?
Rashi: Because the covenant that He made with Avos included punishing the Egyptians for enslaving their children. 1
What are the implications of "Eitzim" that the Kohen places on the fire-pile?
Rashi (in Yoma, 22a): These are two logs as long as the width of the Ma'arachah.
What is the definition of "Boker"? Until when may the Tamid be brought?
Targum Yonasan: "Boker" is until four (seasonal) hours have passed (a third of the day). 1
Like the opinion of R. Yehudah in B'rachos, 26b.
What does the word "v'Arach Aleha ha'Olah" imply?
Rashi Yashan: Based on the 'Hei' at the beginning of the word, it implies importance, and teaches us that the Olas Tamid is always the first Korban to be brought each morning. 1
See Sifsei Chachamim.
Why does the Torah insert the word "Aleha" (in "v'Arach Aleha Chelvei ha'Shelamim")?
Rashi #2 (in Pesachim): To teach us that, if Shelamim is brought, it must be brought after the Tamid shel Shachar, and not after the Tamid shel bein ha'Arbayim. 1
In other words, the Korban Tamid shel bein ha'Arbayim is the last Korban to be brought each day.
Why does it say "veha'Esh"?
Moshav Zekenim: It says so in two other places - "veha'Esh Yardah meha'Shamayim" (Divrei ha'Yamim 2:7:1), and "meha'Esh Yatza'u veha'Esh Tochlem" (Yechezkel 15:7). These hint that Nadav and Avihu correctly brought fire, even though it comes from Shamayim, but they were liable for ruling in front of their Rebbi (according to the opinion that this was their mistake).
Rashi writes that ha'Olah teaches that the Olas Tamid must be the first Korban each day. Above (3:5), we learned this from "Al ha'Olah Asher Al ha'Etzim"! And in Zevachim (89a), we learned this from "Milvad Olas ha'Boker"!
Moshav Zekenim: Ha'Olah teaches that it is the first be slaughtered. Milvad Olas ha'Boker teaches that it is the first to be offered (Haktarah). 1
Moshav Zekenim citing R. Chaim Kohen: From ha'Olah we learn [precedence] only when both of them are Tadir, e.g. the Tamid precedes the Minchah, i.e. Chavitim. 2