Why does the Torah mention lighting a fire over and above all the other Melachos?
Rashi #1 and Ramban #1 (citing Shabbos, 70a): According to R. Yossi, it is to teach us that lighting a fire is only a La'av and is not subject to Kareis.
Rashi #2 and Ramban #2 (Ibid.): According to R. Nasan, it is to teach us that one is Chayav on Shabbos for each Melachah that one transgresses - and not only if one transgresses all thirty-nine.
Ramban #3 and Rashbam: To teach us that the prohibition of Melachah on Shabbos extends even to Ochel Nefesh. 1
Seforno: To teach us that one is Chayav, 2 even though lighting a fire is normally a Kilkul (destructive), for which one is generally Patur on Shabbos,
Moshav Zekenim (citing Bechor Shor), Da'as Zekenim and Hadar Zekenim: Becouse lighting a fire does not seem seem to be a Melachah (and people would therefore say, 'Let us make a fire or prepare coals on Shabbos, so that we can work in gold and silver after Shabbos' - Da'as Zekenim and Hadar Zekenim).
Moshav Zekenim (citing the Rosh): Because it is a Melachah that everyone need to perform.
Erech Apayim 2 (va'Yosef Avraham 5, from the Zohar): Because "Eish" refers to anger, and even though it is always forbidden, on Shabbos one may not display anger on one's face [even if he feels calm].
Kli Yakar (citing Shabbos, 11b): It hints at the punishment for Chilul Shabbos - conflagration. 3 9: Shabbos, 20a: It teaches us that the prohibition of lighting a fire (and burning on it) is confined to private use, but is permitted with regard to burning the fat-pieces and limbs of Korbanos.
Rashbam: As opposed to Yom-Tov, where lighting a fire in order to cook is permitted (See Sh'mos 12:16), regarding Shabbos, the Torah, in Sh'mos 16:23, requires that one prepares one's food before Shabbos. See also Ramban.
Seforno: This is because lighting a fire is needed for the performance of most other Melachos.
Ramban: As the Navi specifically writes in Yirmiyah, 27:17.
Why does the Torah add "be'Chol Moshvoseicham"?
Shabbos, 20a: To extrapolate that one may light a fire to burn the limbs and the fat-pieces that go on the Mizbe'ach. 1
Yevamos, 6b: To teach us, via Gezeirah Shavah from Masei, 35:29 "Vahayu Eileh lachem le'Chukas Mishpat le'Doroseichem" that just as 'Moshvos' there is referring to Beis-Din, so too, here, and that consequently, Misas Beis-Din (S'reifah) does not override Shabbos. 2
Seeing as the Torah is talking about Shabbos, why does it add the words "be'Yom ha'Shabbos"?
Yerushalmi Beitzah, 5:2: To extrapolate that on Yom-Tov on is permitted to light a fire. 1
Mechilta: To extrapolate that one is permitted to light a fire on Erev Shabbos even though it continues to burn on Shabbos. 2
Why do we not say "Kol ha'Oseh vo Melachah Yumas" is a Klal, "Lo Seva'aru" is a Prat, and a 'K'lal u'Ferat' teaches only the P'rat, but not any other Melachah?
Moshav Zekenim: Because, since the Torah does not write 'Kol ha'Oseh Kol Melachah Yumas', it cannot be coming to teach us about the Klal.
