Why does the Torah spell "Yadchah" with a 'Hey'?
Rashi (to 13:9) and Targum Yonasan: Because then it is a contraction of 'Yad Keihah' (the weak arm), indicating that the Tefilin Shel Yad must be worn on the left arm. 1
Menachos 37a: To teach us that even someone whose lower arm is severed is Chayav to put on Tefilin. 2
Oznayim la'Torah (to 13:9): Refer to 13:9:4.1:1.
What is the meaning of "Totafos"?
Rashi #1 (citing Menachos 35b): It is the acronym of 'Tat' and 'Pas,' the former being the Caspian word for two, and the latter, the African word for two, adding up to the four Parshiyos 1 that comprise the Tefilin Shel Rosh. 2
Rashi #2 (citing Menachem ben S'ruk) and Ramban: It is an expression meaning speech. 3 It is similar to the term "Zikaron" mentioned in the first Parshah of the Tefilin (13:9) - one who sees the Tefilin Shel Rosh 'bound between the eyes' will remember the miracle and talk about it.
Ramban: It is named after a Totefes - the name of an ornament that women wear on the forehead from ear to ear. 4
Targum Onkelos and Targum Yonasan: "Totafos" is synonymous with 'Tefilin.'
Menachos 35b (according to R' Yishmael): We learn the four Parshiyos of Tefilin from the three times that the Torah mentions the word "l'Totafos" - here, and in Parshas Va'eschanan, Devarim 6:8 - both minus the second 'Vav;' and in Parshas Ekev, Devarim 11:18 - with a second 'Vav' (plural) - implying two Parshiyos. 5
Maharal: Refer to 13:9:12:1 and its notes.
Oznayim la'Torah (to 13:9): "Totafos" is from the expression 'l'Hatif' (to let drip). Refer to 13:9:4.1:1.
See also Ba'al ha'Turim.
Menachos 34b: This is the opinion of R. Akiva. See answer #5.
Rashi: As we find in Yechezkel 21:2, and in Michah 2:6.
Ramban: See Shabbos 57b. "Totafos" here is in the plural, because of the four compartments that it comprises. See Torah Temimah, note 66, who elaborates.
See Torah Temimah, note 66.
What is the meaning of the Mitzvah of Tefilin?
For an extensive discussion of the Mitzvah of Tefilin according to Maharal, see our commentary to Pasuk 13:9.
We are commanded to don Tefilin, because Hashem brought us out with "Chozek Yad" (a strong hand). What is the significance of this term?
Maharal: Refer to 13:3:3.1:1, and to Shemos 6:1:3.3.
Why is it important to remember Yetzi'as Mitzrayim?
Ramban #1: Because Hashem declines to perform miracles for the Resha'im and deniers in every generation (like He did for Pharaoh). Therefore, He strictly 1 commanded us to remember the miracles of Egypt in all different ways (including wearing it on our arms and on our head, fixing it on our doorposts and mentioning it daily with our lips) - as a constant reminder, never to be forgotten. 2
Ramban #2: Because acknowledging the big, open miracles leads a person to believe in the hidden 'natural' ones, 3 which are part and parcel of every-day life.
Maharal: Refer to 13:3:1.2:1.
Even to the point of sometimes punishing with Kareis (like we find by Chametz and the Korban Pesach).
Moreover, remembering the miracles of Yetzi'as Egypt forms the basics of Emunah (refer to 8:18:2:1 and its note). See Ramban, who elaborates at great length on this issue.
Ramban: And a person who believes that nature takes its own course (and is not the manifestation of Hashem's will) does not have a portion in the Torah (See Ramban, DH 'u'Min ha'Nisim ha'Gedolim'). This is particularly relevant, bearing in mind that nobody was around when Hashem created the world, whereas all of Yisrael witnessed the miracles in Egypt. Note - we also find the corollary between Yetzi'as Egypt and Ma'aseh Bereishis by Shabbos, where we refer to the former in the night Kidush, and the latter, in the morning Kidush.