What exactly, did the brothers see?
Rashi #1: They saw the honor that was afforded to him, and that he was their brother, since he was circumcised like them. 1
Targum Onkelos and Targum Yonasan, Rashi #2: They saw (figuratively) that he was speaking to them in Lashon ha'Kodesh.
Why did Yosef mention Binyamin separately?
Rashi (from Megilah 16b): To hint that, just as he bore Binyamin (who had not participated in the sale) 1 no grudge, so too did he bear his other brothers no grudge.
Ha'amek Davar: Yosef told his brothers to see all his honor. Perhaps they will not see it, for they do not view him favorably - Binyamin sees properly, favorably.
The Seforno explains that Binyamin did not know about the sale. The Midrash however, maintains that he knew about the sale (via Ru'ach ha'Kodesh), but that he chose not to divulge it to his father.
What is the significance of the fact that "his mouth was speaking to them"?
Rashi: He pointed out to them that he was now speaking to them in Lashon ha'Kodesh, 1 and that he no longer required an interpreter. 2
Ramban #2: He was telling his brothers to inform their father that all that they had seen, his Kavod and the power that he enjoyed. And he was now instructing them personally to bring him down as soon as possible, since he was able to support him during the famine.
Rashbam #2: He was instructing them to tell their father, that the news they were giving over to him was not second hand (in which case one is unsure if it is true - Hadar Zekenim), but they had heard it directly from him.
Ramban (from Megilah 16b): It is as if he said, 'like my mouth, so is my heart.' Just as he spoke to them without malice, so too did he hold nothing against them in his heart. 3
Riva, citing R' Aharon of Cologne: Know that I am at peace with you - our family does not speak insincerely. Refer to 37:4:1:1.
Malbim: I may not tell [all] my own praise. Ha'amek Davar - "Yehalelcha Zar v'Lo Ficha" (Mishlei 27:2). Therefore, look to see more than what I tell you, [and tell father].
But the Ramban maintains that Lashon ha'Kodesh is Lashon Kena'an, in which case the fact that he spoke it too, would not have proved anything (See Ramban, 'v'Rabim b'Mitzrayim).' Gur Aryeh addresses this; refer to 45:12:1.4.
As he had until now (Rashbam). And at the time of the sale there was nobody who spoke their language present other than them, since the purchasers were Yishma'elim (Seforno). (I.e. no one else would know that they sold him - PF.)
QUESTIONS ON RASHI
Rashi writes: "'Behold, your own eyes see...' - my honor; and that I am your brother, for I am circumcised just as you are. Also, '... my mouth is speaking to you' - in Lashon Kodesh." Why does Rashi insert all this into the translation of the Pasuk?
Gur Aryeh: One would not say, 'you see that it is I speaking to you;' but rather, 'you hear that it is I....' Therefore, Rashi must insert what it was that they were supposed to see.
Rashi writes: "'Behold, your own eyes see' - ... that I am your brother, for I am circumcised just as you are. Also, '... my mouth is speaking to you' - in Lashon Kodesh." How does Rashi derive that there were two distinct signs that they were supposed to see?
Gur Aryeh: Had there been only one sign, Yosef would have specified what it was. When the Torah leaves a matter unspecified, it refers to more than one thing. 1
Gur Aryeh: Compare to 12:1:2.1:1.
Rashi writes: "'Behold, your own eyes see' - my honor." What was Yosef trying to tell them?
Gur Aryeh: Yosef instructed the brothers to tell Yaakov to descend and join him in Egypt (45:9). Yosef emphasized that he indeed had the wherewithal to benefit them and provide for them.
Rashi writes: "'Behold, your own eyes see' - ... that I am your brother, for I am circumcised just as you are; also, '... my mouth is speaking to you' - in Lashon Kodesh." How do these prove that he is really Yosef? The descendants of Yishmael and Keturah were also circumcised; and many Canaanites knew Lashon Kodesh?
Gur Aryeh #1 (citing Mizrachi): Any other nation that possessed one of these signs, lacked the other (e.g. the Yishmaelim, although circumcised, spoke their own language and not Lashon Kodesh). The combination of the two signs proved that this must be Yosef.
Gur Aryeh #2: Milah is a sign that is on a person's self. Likewise, language identifies a person's self. These constitute sufficient proof. 1
Gur Aryeh: To draw a parallel, testimony to identify a woman's husband as deceased is acceptable only upon the witness recognizing his face; merely recognizing his clothing is not sufficient (Yevamos 120a). We may derive that identity is established by factors that are intrinsic to the person's self, and not merely circumstantial. (EK)
Rashi writes: "'Behold, your own eyes see' - ... that I am your brother, for I am circumcised just as you are; also, '... my mouth is speaking to you' - in Lashon Kodesh." Why couldn't he prove that he was Yosef simply by furnishing details of how he had been sold?
Gur Aryeh #1: Yosef in fact had mentioned at the outset (45:4) that they had sold him. However, the brothers could have claimed that he had merely heard the story from [the real] Yosef. Therefore, Yosef needed these proofs.
Gur Aryeh #2: A story is circumstantial; whereas Milah and language are intrinsic to the person. (Refer to 45:12:1.4:2*.)
Rashi writes: "'Behold, your own eyes see' - ... that I am circumcised just as you are; also, '... my mouth is speaking to you' - in Lashon Kodesh." But earlier, Yosef mentioned only the Milah (Rashi to 45:4), not his language? And why does Yosef say again now that "your own eyes see... that I am circumcised;" they had already seen this (Rashi ibid.)!
Gur Aryeh: Clearly, Yosef was speaking to them in Lashon Kodesh even from the outset (45:4); they would realize this without him pointing it out. Now, Yosef was saying something else - that they were to relate these two signs to Yaakov, so that he too would know that it is truly Yosef. That is why Yosef needed to specify these again here.
Rashi writes: "'Behold, your own eyes see' - ... that I am circumcised just as you are." But this proves nothing, because all of Egypt had circumcised themselves at the onset of the famine (Rashi to 41:55)!
Gur Aryeh #1: Yosef's proof of his identity was the combination of the Milah and Lashon ha'Kodesh (45:12:1.4:1)
Gur Aryeh #2: How would it be possible that the entire Egyptian people suddenly circumcised themselves; unless [the real] Yosef was behind it? This in itself proves that the viceroy was Yosef.
Also refer to 45:4:151.
