Why did he say "Leimor"?
Ohr ha'Chayim #1: Yehudah requested Yaakov to answer him [whether or not he agrees to let Binyamin go].
Ohr ha'Chayim #2: "Leimor Ha'ed" means that he warned us in front of witnesses.
Ohr ha'Chayim #3: Do you have an answer for us to give to the viceroy?
Ohr ha'Chayim #4: This hints to another reason [that Yehudah said] - Shimon is in danger. He is a guarantor, that we will prove that we are not spies!
Why did he say "Ha'ed He'id"?
Malbim 1 : He warned that (a) he will punish us if we come without Binyamin. And even though we could accept punishment, (b) we cannot see him [to buy grain] without Binyamin. Therefore, if we cannot take him, there is no reason to go.
Ha'amek Davar (to 43:3,5) explains similarly, but he holds that the warning was only about punishment. He informed them that without Binyamin, they will not see him.
QUESTIONS ON RASHI
Rashi writes: "'Bilti' - Do not appear before me without your brother. But Onkelos translates, 'unless if your brother is with you' ... he did not precisely translate the verse literally." What did the Targum change?
Gur Aryeh: Onkelos translates the word "Bilti" as 'only.' He therefore must insert a word, "only if (lit. when) your brother is with you."