What are "Karmeha"?
Rashi citing Targum Yonasan: Her leaders. This is like "Lo Yifneh Derech Keramim" (Iyov 24:18) "Karmi Sheli Lo Natarti" (Shir ha'Shirim 1:6).
Rashi: They are vineyards [for Tzadikim]. Hashem will bring Yisrael to the Midbar of Sichon and Og and judge the Resha'im (refer to 2:16:2:2); the Tzadikim will receive like it says in this verse.
Radak: Her vineyards. She will get back her land, like it was. Since the punishment mentioned "va'Hashimosi Gafnah" (14), the consolation mentions her vineyards.
Malbim: Her vineyards. He will return to love his wife, like when she was faithful to him, and return to her the vineyards that he took from her due to her Zenus.
Malbim (according to the Nimshal): (a) It is the sustenance and needs [of Yisrael in the Midbar]. Based on nature, in Galus they lack all good, for they cannot buy fields and vineyards and great acquisitions. They will get all that they lack, only via Hashem's wondrous Hashgachah. (b) These are vineyards of the Nefesh ? Torah and Emunah for which they forfeited their lives in Galus, in days of Shmad - "Karmi Sheli Lo Natarti" (Shir ha'Shirim 1:6).
Why will "Emek Achor" become Pesach Tikvah?
Rashi: The depth of afflictions, which are Achurim (cloudy), will be] an opening of hope ? amidst them, she will put to her heart to return to Me.
Radak: When they first entered the land, this sin of Achan ("Achartanu" ? Yehoshua 7:25) occurred. Emek Achor will no longer be called so ? it is a derogatory name. Rather, it will be called Pesach Tikvah, for praise. He promises them that they need not fear when they return to the land ? they will be purified in Midbar ha'Amim, and Tehorim. It is called Pesach, and not Emek, for it will like be an opening - from there they will enter the land. They will have a good end and hope.
Radak citing Ibn Ezra: Emek Yizre'el, where I troubled them, will revert to be Pesach Tikvah.
Radak citing Rav Sadya Gaon: Hashem will do wonders in the valley where Achan was killed; it will be called Pesach Tikvah.
Malbim: In the end of days, Hashem will remove from them the hardships of subjugation. They will find grace and Chesed everywhere in their Galus, and begin to hope for freedom and redemption.
What is the meaning of "v'Ansah"?
Rashi: It is an expression of dwelling, like "Me'on Arayos" (Nachum 2:12).
Radak citing Rav Sadya Gaon: They will sing [over the wonders that Hashem will do there]. This is like "va'Ta'an Lahem Miryam" (Shemos 15:21).
Malbim: Will return (the miracles done for them in earlier days).
When was her youth?
Rashi: The many days that she dwelled in Egypt.
Radak: It was in the days of Sisero. Also then they sang over the miracle that Hashem did ? "va'Tashar Devorah" (Shoftim 5:1). Also David, "va'Ydaber David la'Shem Es Divrei ha'Shirah ha'Zos" (Shmuel II, 22:1).
Malbim: This refers to miracles done for them in earlier days, e.g. conquering the land and when the Mikdash was built in the days of Shlomo, and k'Yom Alosah ? in Egypt and at Yam Suf.
What is the comparison to ascending from Egypt?
Rashi: She screamed to Me from Egypt, amidst subjugation, and I redeemed her ? also now!
Radak: Also then, they sang after Keri'as Yam Suf.
Malbim: When Yisrael left Egypt, He took them to the Midbar. There they received Torah and Emunah, and they were under His special Hashgachah. They saw His signs and deeds. Zonim are not found there, for the Ma'arachah does not influence good in a Midbar "uv'Sohu Yelel Yeshimon" (Devarim 32:10). Based on nature there is no bread, water, vines or fig tree there.