What did Hashem mean when He said "Ani A'avir Kol Tovi Lefanecha"?
Rashi: He meant that He would pass His full Midah of Goodness before Moshe.
Ramban: Hashem would pass His full Midah of Goodness before Moshe - giving him an insight greater than any other person would ever have 1 - but He would not show him the Shechinah as he requested.
Seforno: He meant that he would do as Moshe asked and pass before him all His goodness.
Oznayim la'Torah: He meant that Moshe and Yisrael should learn from His Midos and go in his ways. 2
Which explains why the Pasuk in Bamidbar 12:7 writes about him "be'Chol Beisi Ne'eman Hu".
Oznayim la'Torah: And from the fact that Hashem first informed Moshe that He had accepted his request and then pointed out the reservations we can learn always to present the positive side of the answer before the negative one, and then, if possible, to explain the good aspect of the refusal, just as Moshe concluded 'Ki Lo Yir'ani ha'Adam va'Chai".
What did Hashem mean when He said "Vekara'si be'Shem Hashem Lefanecha"?
Rashi: He showed Moshe Himself wrapped in a Talis 1 reciting the thirteen qualities of Mercy, and told him that whenever Yisrael are in trouble, they should take their cue from Him and do likewise - because when they call out "Rachum ve'Chanun ... ", they will always be answered.
Ramban: He meant that He would call out His Name (Havayah), but Moshe would not be able to see Him. 2
Seforno: He meant that He would call out His Name - as per his request - to demonstrate that it was not because He does not want to grant his request that Moshe will not see Hashem's full glory, but on account of his limited capacity, and consequently, Moshe will attain part of his request.
Moshav Zekenim #1 (in Pasuk 17): He meant that He would show him the whole Ma'aseh Merkavah from the back, but a person cannot see from the front and live. What He decreed that a hunan-being can see, He will show Moshe. 3
Moshav Zekenim #2 (citing the Rosh): He meant that He will will call His great name, which Moshe cannot see.
Moshav Zekenim #3 (in Pasuk 19): He meant that He will show him how to pronounce the four-letter name of Havayah.
Hadar Zekenim and Rosh: He meant that He will make His Midos known 4 to Moshe, and place his mind at rest.
Refer to 34:6:0.1:1 and see Ba'al ha'Turim.
As the next Pasuk states.
Moshav Zekenim: because a person cannot see from the front and live. What He decreed that a hunan-being can see, He would show Moshe.
"A'avir" is an expression of announcing, as in Vayakhel, 36:6 "Vaya'aviru Kol ba'Machaneh".
What did Hashem mean when He said "ve'Chanosi es Asher Achon ve'Richamti es Asher Aracheim!"?
Rashi, Ramban, Da'as Zekenim, Targum Onkelos and Targum Yonasan: He meant that He will be gracious (favor) when He wants to be gracious, and compassionate 1 when He wants to be compassionate. 2
Rashbam: There (when Hashem's Goodness will pass before Moshe), He will demonstrate His Midos to him.
Seforno: He meant that He would bestow upon Moshe the grace that He bestows upon whoever finds favor in His Eyes in full measure 3 and have mercy on him (as He was merciful to whoever was worthy of His Mercy) to prevent him from being killed by the powerful shine of His Glory. 4
Moshav Zekenim #1: He meant that through what Hashem is about to announce, Moshe will know the level of grace and mercy people receive through His name.
Moshav Zekenim #2: He meant that, once one mentions this name with its correct pronunciation, Hashem will have all the mercy upon him as He will ever have.
Even with someone who is not worthy, since "Chanun by definition means a free gift (B'rachos, 7a). See Torah Temimah, mote 23.
He would understand Hashem's Midos of Chaninah and Rachamim, even though he would not be able to see Him personally (Ramban).
Limited by his (Moshe's) inability to accept it in full - as the next Pasuk goes on to explain.
Why is it necessary to recite the thirteen Midos? Why will Z'chus Avos not suffice?
Rashi: Because the thirteen Midos will take effect even when Z'chus Avos is no longer effective.