Why does the Torah add the word "Izim"?
Chulin 113a-b: To teach us that, wherever the Torah does not specify (e.g. regarding meat and milk) "Gedi" can be even a cow or a sheep.
Why did Yehudah send the kid?
Malbim #1: He wanted to fulfill his word. If so, one need not search for her. If he sent to her place, and she went away, he fulfilled his word.
Malbim #2: He wanted to get back the security. If so, one must search for her. Within this, there is a distinction. (a) If he wants it back because they are worth more than the kid, or because it is a bad Siman to lend a signet ring, the Shali'ach should pursue and ask about her, even if there will be some shame when it is found with a harlot. (b) If, however, he wants the security to avoid shame, lest a harlot boast that she has Yehudah's ring for an Esnan, he should not investigate, for this will surely bring shame! 1 Chirah erred, and thought that Yehudah wanted the security for itself. Yehudah corrected him; I was concerned for shame, so do not investigate more. I fulfilled my word; she deviated, by leaving!
Ha'amek Davar: To Yehudah, the kid was worth nothing compared to the security. For her, it was opposite. What do these things do for her?
Why must this bring shame to Yehudah? The Shali'ach merely asked if people knew about a harlot. He did not say that Yehudah had Bi'ah with her! People will assume that the Shali'ach did! Perhaps Yehudah was concerned for Chirah's shame. Or since they were known to be friends, people would suspect that he was Yehudah's Shali'ach, especially if Chirah was not a shepherd (and was unlikely to offer a kid for an Esnan). Yehudah said, "let we be shamed" (38:23 - PF).
Yehudah promised to send "Gedi Izim." Why did he send "Gedi ha'Izim" (with the definite article)?
Ha'amek Davar: He recognized her esteem, and sent her a choice kid.
