What are "ha'Ge'ulah" and "ha'Te'udah"?
Rashi citing Bava Metzi'a 47a: "Ge'ulah" refers to a sale; "Te'udah" refers to Chalipin (a swap).
What is the significance that he gave his shoe?
Torah Temimah citing Bava Metzi'a 47a: Chalipin works only with a Kli.
Malbim citing Rus Rabah 7:11: They used to acquire with a shoe or sandal - "Shalaf Ish l'Re'ehu." They switched to acquire via Ketzatzah. If one sold his field to a Nochri, his relatives take a barrel of parched grain and nuts and break it in front of children. The children gather, and say 'Ploni is lost from his family.' They did the same for one who married a woman of improper lineage 1 . They returned to acquire with a shoe or sandal - Shalaf Ish l'Re'ehu. They returned to acquire via money, a document or Chazakah.
Kesuvos 28b says so.
What do we learn from "v'Zos Lifnim b'Yisrael"?
Malbim: Mi'Lifnim refers to something that applies now, it applied also in olden days. Lifnim teaches that it used to apply, but not after, e.g. "ha'Emim Lefanim Yashvu Vah" (Devarim 2:10). This shows that the Kinyan ceased afterwards! Something that returns to the giver is not acquired via Chalipin. In the days of Yehoshua they acquired [even land] with Chalipin. After the first Yovel, people saw that land returns, so they switched to Ketzatzah (refer to 4:7:2:2). Ketzatzah was also used for one who married a woman of improper lineage. They could not use it now, lest people say that Rus was forbidden! Therefore, he returned to use Chalipin 1 ; what is acquired via Yibum does not return (Bechoros 52b).
Presumably, Malbim explains that Chalipin was not used for normal transfer of land until Yovel ceased. (PF)
What do we learn from "v'Nasan l'Re'ehu"?
Rashi citing Bava Metzi'a 47a #1: In Kinyan Chalipin, the buyer gives the Kli. Bo'az (who acquired rights to redeem the field) gave to the Go'el.
Rashi citing Bava Metzi'a 47a #2: The seller gives the Kli. The Go'el gave to Boaz.
Torah Temimah citing Bava Metzi'a 7a: If one grabs three fingers by three fingers of a garment (given for Kinyan Chalipin), he acquires. We consider the garment to be cut (and this fulfills "v'Nasan l'Re'ehu").
What is the meaning of "v'Zos ha'Te'udah b'Yisrael"?
Rashi: It is the law of testimony.
Malbim: Since this Kinyan worked earlier (refer to 4:7:3:1 and the note there), it works also now, that we cannot use Ketzatzah.