What is the significance of the juxtaposition of "Shiv'as Yamim" to "Tishmor?
Chagigah, 18a: It implies that that Chol ha'Mo'ed is included in the Isur Melachah on Yom-Tov. 1
See Torah Temimah, note 97, who discusses a. the fact that Chazal actually learn this from "es Chag haa'Matzos Tishmor" in Ki Sisa, 34:18, and b. whether the Isur Melachah on Chol ha'Mo'ed is perhaps only mi'de'Rabbanan, and the D'rashah from the Pasuk is merely an Asmachta.
Why is Nisan called "Chodesh ha'Aviv"?
Rashi #1: Because it is the month when the grain ripens on its stalks ('be'Ivehah'). 1
Rashi #2: Because it is the father of the months, in that it is the month when the fruits first ripen. 2
Seforno: Because one should make sure that Pesach always falls in the month of Aviv, 3 by declaring leap-months and leap-years when necessary. 4
Sifri (in Devarim 16:1): Hashem deliberately took us out of Egypt in the month of spring, the ideal month to travel, since it is neither too hot nor too cold. 5
Refer to 23:15:1.1:1.
It is also generally translated as 'the month of spring'. See answer #4.
The commentaries poinnt out that the acronym of "Aviv" is 'Av - Yud Beis' (12), because it is the first of the twelve months.
See also Re'ei Devarim, 16:1.
As the Gemara explains in Rosh Hashanah, 21a (Seforno).
What are the implications of "le'Mo'ed Chodesh ha'Aviv"?
Mechilta: It implies that Pesach must fall in the spring. Consequently, in order to ensure that it does, it is sometimes necessary to declare a leap-year.
What are the connotations of "ve'Lo Yera'u Panai Reikam"?
Rashi: It means that when performing the Mitzvah of Aliyas ha'Regel, one should take Olos 1 to the Beis-Hamikdash to give to Hashem. 2
Oznayim la'Torah: It is to commemorate Yetzi'as Mitzrayim, where Hashem told Yisrael "Lo Seilchu Reikam" - that they left Egypt with great wealth. And the obligation of appesaring extends also to Shavu'os and Sukos, which are also 'Zeicher li'Yetzi'as Mitzrayim.'
Chagigah, 7a: Specifically Olos - which are fitting for Hakadosh-Baruch-Hu, just like a Chagigah consists of a Shelamim, which is fitting for a Hedyot. See also Torah Temimah, note 100.
Chagigah, 7a: One only transgresses the La'av however, if one appears in the Beis-Hamikdash without a Korban on the first day of Pesach, not on any of the other days.
What are the implications of "Reikam"?