What was the significance of the ornaments that Eliezer gave Rivkah?
Rashi and Targum Yonasan: The nose-ring (that weighed a Beka (half a Shekel) hinted at the half-Shekel 1 that Yisraelim give every year for Korbanos Tzibur; the two bracelets (Tzemidin) of weight ten gold Shekalim, hinted at the two Luchos (Metzumados - exactly similar), and Aseres ha'Dibros that were engraved on them.
Why did Eliezer give the ornaments to Rivkah before he knew that she was from the right family?
Rashi (on Pasuk 23): Because, on the merit of Avraham, he felt certain that Hakadosh-Baruch-Hu had granted him success. 1
Rashbam, Da'as Zekenim and Ramban: He actually asked her first about her family, only the Torah inverts the order, because it wants to first finish telling us what Eliezer did and her response (Rashbam). 2
Malbim: He was not required to find a girl from Avraham's family. Ha'Emek Davar
This is borne out by what Eliezer told Rivkah's parents (See Pasuk 47). The Ramban, on the other hand, proves his point from the fact that the Torah omits the verb "and he placed", implying that he only took the ornaments out, but did not give them until after he had asked her about her family.
Perhaps this is because the Gemara said only that he prayed improperly, lest she have a blemish. It did not say, lest she not be from Avraham's family! (PF)
Why does it say that the bracelets were on her hands? It does not even say that he gave them to her!
Ohr ha'Chayim: They fit her hands perfectly