Why did Noach curse Kena'an, if it was Cham that sinned?
Rashi and Targum Yonasan: Since Cham caused Noach to be incapable 1 of having a fourth son, 2 Noach cursed Cham's fourth son.
Seforno: It was Kena'an who had perpetrated the deed; Cham is condemned by the verse for remaining silent. Refer to 9:22:1:4; refer to 9:22:1:5.
Moshav Zekenim, Riva #1, Rosh: Since HaSh-m blessed [all who left the Ark, including] Cham (9:1), Noach could not curse him. 3
Hadar Zekenim, Riva #2: It was Kena'an who saw Noach unclothed, and told Cham. 4
According to the opinion that Cham castrated Noach, why did he do so?
Rashi: "Adam ha'Rishon had two sons, who killed each other for their father's inheritance," he pointed out. "And our father already has three sons, and yet he wants a fourth one!" (He castrated him, to prevent this.) 1
See Sifsei Chachamim.
Why was Kena'an punished with servitude specifically ?
Rashi: Noach said, "You caused me not to have a fourth son to serve me, placing the burden on your brothers; may your fourth son be cursed to serve your brothers' descendants."
Da'as Zekenim, Hadar Zekenim, Moshav Zekenim, Rosh: The Navi says, "Ben Yechabed Av v'Eved Adonav" (Malachi 1:6). This may be interpreted as," one who does not honor his father, it is proper for him to be a slave."
Maharal (Gevuros Hashem, Ch. 4 p. 31): Yisrael (descendents of Shem) are Tzurah removed from Chomer, they are truly free. 1 The Kena'anim resemble Tzurah stamped onto base Chomer, they are not free but rather enslaved. 2
This is comparable to the sharp blade at the edge of a knife. The Chomer (material) of the knife needs the Tzurah (form) of the blade to actualize its function. The blade is free to act as it pleases, and the knife must follow.
A stamp emblazoned onto the side of the knife is not free; it serves the knife. Cham was enslaved to his physicality; refer to 9:23:1.2:1. (EK)
Why did Noach use the double expression, "Eved Avadim"?
Seforno: Due to his lowliness, Kena'an was anyway fit to be a slave to his brothers; after this episode, Noach added the title "Eved Avadim."
Da'as Zekenim #1: He cursed both Cham and Kena'an to be slaves to their brothers. Cham should have covered Noach himself. Since he imposed this on his brothers, he will serve them.
Da'as Zekenim #2: He will never go free.
To whom was Noach referring when he said that Kena'an would become a slave of slaves to his brothers?
Ramban #1: He would become a slave to his brethren - the whole of mankind (whoever would find him would be permitted to take and make him do his bidding.
Ramban #2: Shem and Yefes (his father's brothers). 1
Ramban #3 (citing Ibn Ezra and Radak): his own brothers (Put, Mitzrayim and Kush). 2
As we find later (Bereishis 14:14).
In any event, the Ramban points out, if he became a slave to Shem and Yefes and to his own brothers, he became a slave to the whole world.