What are the connotations of "Shabbos la'Hashem Elokecha"?
Rashi and Seforno: One observes Shabbos in honor of Hashem. One learns and teaches on Shabbos, observes and does, and enjoys the Shabbos, 1 all in honor of Hashem.
Seforno: [One eats and drinks special food] in order to serve Him better, as Rava said (in Yoma, 7b) 'Wine and spices made me wise.'
Seeing as one's children are included in the prohibition, what does the Torah mean when it writes "Atah u'Vincha u'Vitecha"?
Rashi, Ramban and Seforno: Although, min ha'Torah, children are not generally included in the Mitzvos, the Torah here is issuing a prohibition against children performing a Melachah on behalf of their parents 1 on Shabbos. 2
Seeing as Avadim and Shefachos have the same Din as women, why does the Torah see fit to warn their masters?
Ramban #1: Since Avadim are under the jurisdiction of their masters, the Torah holds the latter responsible to keep them in check.
Ramban #2: Because Hashem is saying the Aseres ha'Dibros to Yisrael and not to the Avadim.
What are the ramifications of u'Vehemtecha"?
Rosh #1, Torah Temimah (citing Shabbos, 153b, 154a): It is a Lav against Mechamer (making an animal work, e.g. leading it when it is laden) on Shabbos. 1
Rosh #2: One may not lend his animal to a non-Jew (to work on Shabbos, for he is commanded that his animal rest. If he lent it before Shabbos, he must make the animal Hefker.
Rosh: Even though there is no Misah for Mechamer, it is not subject to Malkos, because the same Lav warns against doing Melachah, which has Misas Beis-Din.
To which sort of Ger does the Pasuk here refer?
Ramban #1: It is referring to a Ger Toshav, 1 who has undertaken to keep the seven Mitzvos b'nei No'ach. He is not obligated to keep Shabbos, but is forbidden to perform Melachos on behalf of a Yisrael. 2
Whom the Gemara in Avodah-Zarah (64b) refers to as 'Ger Ochel Neveilos' (See Ramban).
Ramban: Just like a minor and an animal. It is later in Shemos (23:12) that the Torah issues a warning against Chilul Shabbos to a Ger Tzedek.
Ramban: Whereas the Pasuk below (23:12) refers to a Ger Toshav, which explains why it compares him to an animal. See also Devarim (5:14).
Rosh: Why must a Ger Tzedek be taught? He is a full Yisrael, for he accepted all the Mitzvos! One might have thought that Shabbos is so dear to Hashem, that it is only for one who was conceived in Kedushah.