Why will Hashem punish the family of the sinner? What did they do wrong?
Rashi and Targum Yonasan: Because inevitably his family cover-up for him. 1
Seforno: Because the 'people of the land' would not hide their eyes from the sinner, if his own family did not support him.
Rashi (Ibid.): 'There is no family in which there is a publican (an illegal tax-collector) whose members are not all publicans' (and there is no family in which there is a robber and they are not all robbers - Shevu'os, 39a). See Torah Temimah, note 7.
"Vesami Ani es Panai ba'Ish ha'Hu u've'Mishpachto". Does this mean that his family are also Chayav Kareis?
Shevu'os, 39a: No! It means that they will smitten with Yisurim (affictions).
What is the significance of the comparison of Kareis bi'Yedei Shamayim to Misah bi'Yedei Adam (See Torah Temimah, note 10)?
Why does the Torah write "Vehichrati oso ... ", (and not simply 'Vehichrativ')?
Rashi and Targum Yonasan: To extrapolate that, although the members of his family stand to be punished, only he is subject to Kareis and not they (and Hashem will punish them with suffering - Targum Yonasan).
What are the implications of "Liznos Acharei ha'Molech ... "?
Rashi: It comes to include other types of idolatry which one worships in this way, 1 even if they are not generally served in this manner. 2
Ramban: It comes to include the Avodah of Molech where one passes the child through the fire in an unconventional manner.
Ramban (DH 've'ha'Beraisa'): As opposed to any other form of worship, for which one is Chayav Misah only if that is the way that the Avodah-Zarah is generally worshipped (or one of the four primary Avodos ha'Mikdash - Shechitah, burning on the Mizbe'ach, sprinkling the blood and prostrating oneself - for which one is always Chayav). And the Beraisa that Rashi cites does not learn this from "Liznos Acharei ha'Molech ... " but from the Chiyuv Kareis, which is otherwise superfluous.
Ramban and Moshav Zekenim: This implies that Molech is the name of a particular Avodah-Zarah that is worshipped in this manner. The Mishnah in Sanhedrin, 64a however, says this only according to the opinion that it is anything that people accept as an idolatry. Refer to 18:21:1:1* & 18:21:1:4.