Why did Noach bear his first son at the age of five hundred, while the rest of the world was doing so at less than a hundred?
Rashi: Had Noach's children been older, if they would turn out to be Resha'im, he would suffer to see them all die in the Flood; whereas if they would be Tzadikim, he would have to build many Teivos. So Hashem stopped him from having children until the age of five hundred, so that even Yefes, the oldest, would not reach the age of a hundred before the flood, and would therefore not be subject to punishment. 1
Based on the Pasuk, "Ki ha'Na'ar ben Me'ah Shanah Yamus" - Yeshayah 65:20 - (as was also the case before Matan Torah). Moshav Zekenim asks that the Pasuk in Yeshayah is written in connection with Olam ha'Ba, and the only difference between this world and the world to come is servitude to the kingdoms - but the age of punishment (from twenty) will not change? See also Sifsei Chachamim.
Seeing as Yefes was the oldest of Noach's sons, why does the Torah invert the order?
Rashi: It first lists Shem, who was the most righteous, was born already circumcised, and from whom Avraham will descend. 1
See Sifsei Chachamim.
How old was Noach when Cham and Shem were born?
Rashi (in Avodah Zarah 9a): He was five hundred and one when Cham was born ,and five hundred and two when Shem was born. 1
See Torah Temimah, citing Sanhedrin 69b, who presents all the deails regarding the ages of Noach's sons and who discusses the current question.
Until now, the Torah mentioned the names of only the Bechor of each successive son of Adam. Why here does it mention all three sons of Noach?
Oznayim la'Torah: Because they formed the three major families from which the whole world developed - as the Torah will specifically state in Parshas Noach (9:19).
QUESTIONS ON RASHI
Rashi writes: "500 years old - ... Hashem said... if [his children] would be righteous, I would be making him bother to build many Arks." Does this constitute a reason to withhold children?
Gur Aryeh: The main reason that Noach did not have children until age 500 was lest they turn out to be wicked. If we argue that Hashem always inclines His judgment toward the good, and so we should follow the possibility that his children would be righteous, we must add that even that side has a slight disadvantage, lest Noach have to build many Arks.
Rashi writes: "500 years old - ... If his children would be wicked, they will be destroyed, and this would be difficult for the righteous [Noach]. If they would be righteous, I would be making him bother to build many Arks. .... Even his eldest son would not be of age for [Divine] punishment before the Flood." In the Midrash, these are two separate opinions, of Rebbi Yudan and Rebbi Nechemyah. It seems that Rashi has blended them together?
Mizrachi: Both opinions agree that any children under age 100 would not be punished. Rebbi Nechemyah is concerned only that they might turn out wicked (and not lest Noach have to build many Arks). Thus, Rashi quotes Rebbi Yudan. 1
Gur Aryeh: According to Rebbi Yudan, wicked sons at any age would have been destroyed. Hashem withheld children from Noach until age 500, to decrease the amount of children he would have. Noach's merits (along with his sons' own merits) were sufficient to save three sons from ever turning wicked; but had there been more children, Noach's merits may not have been enough to influence them. 2 According to Rebbi Nechemyah, however, any son under 100 would not be punished, and that was the primary reason. Rashi is citing Rebbi Nechemyah; only he adds that Hashem did not grant older sons as well (in addition to the younger ones who were assured of survival), so as not to cause pain to Noach should they perish.
Rashi writes: "100 years old... will be of age for [Divine] punishment in the future; and so too prior to the Giving of the Torah." If so, why were Er and Onan punished with death (in Bereishis 38: 7-10)?
Gur Aryeh: This rule refers only to Divine judgment for a particular circumstance that might warrant it, such as at the Flood. However, when the Torah mandates the penalty of Misah bi'Yedei Shamayim for a specific transgression, such as that of Er and Onan, no judgment is necessary, and that minimum age does not apply. 1
Gur Aryeh: The same distinction applies today, when the minimum age for Divine punishment is 20 (Shabbos 89b). Would a young man age 13-20, who eats Chelev, be exempt from Kareis?! Rather, he is only exempt from Divine judgments for particular circumstances (such as at the Meraglim; Rashi to Shabbos 89b).
Rashi writes: "Yefes was the eldest [of Noach's sons]." He is not listed first in this verse, so how does Rashi know this?