What does the Torah mean when it writes that it should be a sign on the arm?
Because later (in Pasuk 16) the Torah writes "Yadchah" with a 'Hey' - the acronym of Yad Keiheh (the weak arm [See also Peirush Yonasan]).
Targum Yonasan (as the Pasuk writes in the second Parshah of Shema [Peirush Yonasan]). In this way, the Tefilin are placed on the head and next to the heart, the dwelling-places of the Machshavah (Ramban, Pasuk 16 [as the Torah writes in Devarim 4:39, "v'Yadata ha'Yom va'Hashevosa El Levavecha"]).
What does it mean when it writes that it should be a remembrance between the eyes?
Rashi: This refers to tying Tefilin on the head.
Targum Yonasan: This refers to writing the miracle inside the Tefilin Shel Rosh, and fixing it opposite the eyes, on the height of the head. 1
See Peirush Yonasan.
What are ramifications of the phrase "Lema'am Tih'yeh Toras Hashem b'Ficha"?
Ramban: Inverting the last two phrases in the Pasuk, the Torah is telling us that by placing Yetzi'as Egypt on our arms and heads, and remembering it at all times, Hashem's Mitzvos will be constantly on our lips, to observe His Mitzvos, since He is our Master who redeemed us from the house of bondage.
Shabbos 108a: Tefilin must be written on hide of an animal permitted to your mouth (a Tahor species, which you may eat).