Why does the Torah declare the Shomer Chayav for Geneivah, when in Pasuk 7, it declared him Patur for Geneivah and Aveidah?
What exactly does "Yevi'ehu Eid" mean?
Ramban (citing Ibn Ezra) and Rashbam: He brings a part of the torn carcass 3 to substantiate his claim.
Seforno. See also Torah Temimah (citing Aba Sha'ul in Bava Kama, 11a, who Darshens 'Yavi Adudah [the carcass] le'Beis-Din).
Because wherever the Torah says "Eid", it means two witnesses (Seforno, citing Sotah, 2a). See also Sifsei Chachamim.
Why will a Shevu'ah not suffice (like in Pasuk 10)?
Ramban #1: In fact, the Din is the same in both cases - If there are witnesses, he brings them to substantiate his claim, and if not, a Shevu'ah will suffice. And the Torah mentions witnesses here and a Shevu'ah above, because when the animal dies in its owner's domain or falls off a cliff 1 or is stolen by armed bandits, in all likelihood there are no witnesses; whereas when a lion or a bear attacks the herd, all the shepherds gather to try and stave it off.
Ramban #2 and Seforno: It is for the same reason that Isi ben Yeehudah, commenting on Pasuk 9, extrapolates from "Ein Ro'eh" that if the Oneis occurs in a location where there are witnesses, then we do not rely on a Shevu'ah.