What are the connotations of "Derachecha"? What is the meaning of "Lema'an Emtza Chein be'Einecha"?
Rashi #1: If he did indeed find favor with Hashem, he wanted to know the reward that this entailed - in order to understand the true meaning of the 'Metzi'as Chein'.
Targum Yonasan: He wanted to know Hashem's method of judgement - Why sometimes Tzadikim receive the dues of Resha'im and Resha'im the dues of Tzadikim, and sometimes the Tzadikim receive the dues of Tzadikim and Resha'im, the dues of Resha'im - because he had found favor in Hashem's Eyes'. ... 1
Rashbam: Moshe was asking Hashem to lead them personally and not via a Mal'ach, 2 because he had found favor ... .
Seforno: He wanted to understand two things: 1. How with His knowledge alone He grants existence to things that exist, and 2. How, in spite of Hashem's knowledge (that does not lie), people still have freewill and choice, in order to find favor with Hashem. 3
Targum Onkelos: 'Tell me now Your way of goodness, and I will know Your compassion, in order that I find favor ... '.
B'rachos, 7a: Moshe said before Hakadosh-Baruch-Hu 'Ribono shel Olam; Why is it that some Tzadikim have it good and some, bad; and why is it that some Resha'im have it good and some, bad?'
See Na'ar Yonasan.
Seforno: As we find in Yirmiyah, 9:23. B'rachos (ibid.): To which Hashem replied; Tzadik ve'Tov lo - Tzadik Gamur; Tzadik ve'Ra lo - Tzadik she'Eino Gamur; Rasha ve'Tov lo - Tzadik she'Eino Gamur; Rasha ve'Ra lo - Rasha Gamur'.
What is the meaning of "ve'Eda'acha b'Shem"?
Rashi #1 and #2: It means that, with that knowledge, Moshe would understand the workings of Hashem's reward (and punishment).
Rashbam: It means "And I will follow You!"
Seforno: It means that, through the knowledge of how Hashem operates, he would acquire a better understanding of Hashem Himself.
What did Moshe mean when he added "u'Re'ei Amcha ha'Goy ha'Zeh"?
Rashi: He meant 'These are Your people since times gone-by, and if You reject them (and accept me), what guarantee do I have on the perpetual existence of my offspring? If you want to tell me about my reward, it can only be in conjunction with this people!'
Seforno: He meant that it is only in the midst of Yisrael that Hashem's Name becomes known in the world, 1 and not in the midst of the other nations. 2
Hadar Zekenim (in Pasuk 14): He meant that he did not know to choose what is good for Yisrael, and that Hashem should choose, since only he knows what is best for them.
Moshav Zekenim #1: He was asking that Hashem should Personaly go with Yisrael for the sake of His Honor.
Moshav Zekenim #2 (in Pasuk 17): To exclude the Eirev Rav who were already finished.
See Tehilim, 76:2 (Seforno).
Seforno: Consequently, it would not be fitting to withhold from Moshe his request for the Shechinah to lead them, despite their sin. See Bava Basra, 134a.