What is the difference between "Kali" and "Carmel"?
Rashi: "Kali" is flour made from soft kernels that were pre-roasted in the oven; "Carmel" is the kernels themselves.
Rashi #2 (Kerisus, 4b): "Kali" refers to corn that has been roasted in the oven; "Carmel", to soft kernels that have been rubbed with the hand. 1
Rashi: "Carmel" is the acronym of 'Rach' (soft) 'Mal' (rubbed).
What are the implications of "Ad Etzem ha'Yom ha'Zeh"?
Rashi (in Menachos, 5b): It implies that one may eat Chadash from the morning of the 16th of Nisan.
What are the ramifications of "b'Chol Moshvoseichem"?
Rashi #1 (citing Kidushin 37a): It teaches us that the Isur of Chadash applies in Chutz la'Aretz 1 , too.
Rashi #2 (citing Kidushin, 37a): It teaches us that the Isur of Chadash will only take effect after they capture Eretz Yisrael and distribute it. 2
Moshav Zekenim: This is the Halachah. It must be planted 33 days before the Omer in order that the Omer will permit it. Ritzva said that in Chutz la'Aretz it applies only to Yisrael's grain, and in Eretz Yisrael, even to a Nochri's. R. Shlomo of Darvash permitted beer in winter [in Chutz la'Aretz], for most of the world seeds (33 days) before Nisan 16, even if most of the country does not. The Halachah follows R. Zeira, who does not require two majorities [he permits meat found in the market, if most stores in the city sell Kosher meat], even if the doors of the city are locked (so we cannot join a majority of passers-by; for lineage, we require two majorities - Kesuvos 15a] (Why do we rely on the world majority, even if the grain is presumably from this country? And how did R. Shlomo know when most of the world sows? See Tosfos Gitin 8a DH R. Yehudah; his answer will not help here! It seems that it is printing mistake; it should say for most of the country seeds (33 days before) Nisan 16, even if most of the world does not. - PF)
Which turned out to be 14 years after they entered it - seven years of conquest and seven years of division.
Why does the Torah insert the phrase "Chukas Olam le'Doroseichem b'Chol Moshvoseichem" here and in connection with the Sh'tei ha'Lechem (in Pasuk 21)?
Ramban, Moshav Zekenim and Seforno: To teach us that the Isur of Chadash and that of desisting from Melachah on Shavu'os, respectively, apply even today (and in Chutz la'Aretz - Seforno on Pasuk 31 in connection with Yom Kipur), when the Omer and the Sh'tei ha'Lechem are no longer brought. 1
Ramban citing Kidushin, 37b: In the same way as it mentions "Moshvoseichem" by Cheilev and Dam (3:17). Ramban and Seforno (in Pasuk 31): And it is for the same reason that the Torah inserts "b'Chol Moshvoseichem" by Yom Kipur - because in Acharei-Mos, the main Kaparah depends on the Korbanos, and we might otherwise have thought that, nowadays, when there are no Korbanos, there is no Kaparah (Refer also to 23:18:1:1). See also Ramban as to why the Torah does not mention "b'Chol Moshvoseichem" here in connection with Pesach, but does mention it in Shemos (12:14, 17).
Nowadays that we cannot offer the Omer, is Sefiras ha'Omer mid'Oraisa?
Seforno (Pasuk 21): B'Chol Moshvoseichem teaches that counting the Omer always applies [mid'Oraisa].
Hadar Zekenim (16): Now it is only to commemorate the Mikdash. After Sefiras ha'Omer we pray that the Mikdash be rebuilt, for then it will be mid'Oraisa.