What is the connection between the Korban Omer and Sefiras ha'Omer on Pesach and the Sh'tei ha'Lechem on Shavu'os?
Ramban: One begins to count the Omer at the beginning of the barley harvest, on the day that one brings the first produce of the barley crops together with a Korban; whereas the Sh'tei ha'Lechem comprises the first produce of wheat, which is also brought together with a Korban. 1
Ramban: Which is secondary to the Minchah regarding both the Omer and the Sh'tei ha'Lechem.
Until when does one count the Omer?
Rashi: One counts the Omer up to the end of the seven-week period 1 - forty-nine days.
Rashi: Because the word "Ad" (in the phrase "Ad mi'Mocohras ha'Shabbos ha'Shevi'is" is exclusive.
What are the connotations of "Minchah Chadashah"?
Rashi: It is the first Korban that is brought from the new wheat crops. 1
Ramban: It is a prohibition against bringing a Minchah from the new crops before the Sh'tei ha'Lechem.
Rashi: Even though the Omer preceded it, the Omer was different, inasmuch as it consisted of barley, whereas all other Menachos (with the sole exception of the Minchas Kena'os of a Sotah) consisted of wheat.
How do the words "Chamishim Yom fit into the Pasuk?
Rashi #1: "Chamishim Yom" goes together with the following phrase, to read "Chamishim Yom ve'Hikravtem Minchah Chadashah la'Hashem".
Rashi #2: One needs to invert "Tisperu" and "Chamishim Yom", in which case "Chamishim Yom" goes together with "Mochoras ha'Shabbos ha'Shevi'is, with which it is synonymous.
Why are the Sh'tei ha'Lechem called "Minchah Chadashah"?
Rashi and Rashbam: Because it is the first Korban that is brought in the Beis-Hamikdash from the new produce. 1
Seforno (on Pasuk 17): The Omer is brought from the first produce of barley, and the Sh'tei ha'Lechem, from the first produce of wheat. 2