What is "Tor"?
Rashi: It is the time.
What is the significance of 12 months?
Vilna Gaon: It is proper to give to a woman 12 months for ornaments 1 . There are many superfluous words in this verse. They hint to the Neshamah, which is called Na'arah. Every Rosh Hashanah 2 and Yom Kipur, a person repents, and screams 'I sinned - pardon me!', and Hashem, amidst His great Chesed and mercy, passes over his sins. The sin is not erased. Only if he will do full Teshuvah, He will pardon it. If he sins later, he will be punished more due to previous sins 3 . They wait 12 months for this.
Malbim: It is possible that a beautiful girl has an internal illness; some show only at certain times of the year. The 12 months are days of Miruk and testing (for such illnesses).
Kesuvos 57a: We give a virgin 12 months to prepare [Rashi - ornaments] for Chupah from when the husband asks to make Nisu'in.
We do not confess on Rosh Hashanah (Magen Avraham 584, from the Zohar). This is why some Poskim say to omit Avinu Malkeinu, or parts of it (Mishnah Berurah 584:3)! (PF)
Vilna Gaon: "Im Banecha Chat'u Lo va'Yshalchem b'Yad Pish'am" (Iyov 8:4) - even though they did only Chet (Shogeg), for which they are not worthy to be expelled, they were expelled due to their prior Pesha'im. The Chet caused punishment for the Pesha. 'In our Chet and our fathers' Avon, the Beis ha'Mikdash was destroyed' - it was destroyed due to their Avon. We should not be liable for our Chet; even so, it is not rebuilt, because our Chet arouses their Avon.
What are "Yemei Merukeihen"?
Vilna Gaon: The days in which they Merik (empty) themselves of sins.
Malbim: Refer to 2:12:2:2.
What is "Shemen ha'Mor"?
Torah Temimah citing Megilah 13a #1: It is satchet.
Torah Temimah citing Megilah 13a #2: It is oil of olives that did not reach one third growth (Anfekinon). Girls anoint with it to make hair fall out 1 and to soften the skin.
Malbim: It warms the limbs; they anoint with it in winter.
Vilna Gaon: Everything in man was created for a need, except for hair. It corresponds to unnecessary matters. A hint to this is Eshes Yefas To'ar - "v'Gilchah Es Roshah v'Asesah Es Tziporneha" (Devarim 21:12), the excesses. For six months he casts off all excess desires, and for six months he gets used to Mitzvos - refer to 2:12:5:1. So he will accustom himself the entire year!
What are "Besamim" [and "Tamrukei ha'Nashim"]?
Vilna Gaon: Besamim are Mitzvos Aseh. Tamrukei ha'Nashim are Lavim; he is Merik (empties) himself from sin.
Malbim: They are fragrances that remove mold found at such times.
