When did Moshe's face begin to shine?
Rashi: When he came down for the last time on Yom Kipur.
What are the connotations of the word "Ki Karan Or Panav"?
Rashi #1: It describes the shine on Moshe's face which resembled horns.
Rashi #2 (in Chavakuk): It describes a ray of light that bursts out and shines through a hole like horns. 1
Rashi #3 (in Pesachim, 8a): It is an expression of 'Zohar' (radiance).
Rashi #4 (in Nidah,19a): It is an expression of 'Nogah' (shine).
Rashbam: It is an expression of splendor. 2
What was the source of Moshe's rays of light?
Rashi #1 (citing Sh'mos Rabah 47:6): From the cave, when Hashem placed His Hand on his face (that he should not see Him as He passed). 1
Rashi #2 (in Koheles, 8:1): "A man's wisdom illuminates his face ... ". 2
Targum Yonasan, Da'as Zekenim and Moshav Zekenim (both in Pasuk 30): It was from the radiance of the Shechinah (from when Hashem spoke with Moshe - Targum Yonason).
Hadar Zekenim (in Pasuk 35), Rosh and Riva: When Moshe was writing, he would clean the quill on his hair. 3
Sh'mos Rabah 47:6: When Moshe was writing, a small amount of ink remained 4 on the quill, and he wiped it on his brow, from which his face radiated
Sh'mos Rabah 47:6: Some say that Hashem was holding two Tefachim of the Luchos, Moshe held two Tefachim on the other end, and he received radiance from the middle two Tefachim.
See also Ba'al ha'Turim and Or ha'Chayim, Pasuk 28, DH 'u've'Midrash'.
Moshav Zekenim (30) cites this Pasuk, but also says that it was from remnants of the stylus that he used to write the second Luchos. He retracts from this however, since Hashem wrote them.
Hadar Zekenim, Rosh and Riva: That is why the custom is for scribes to do so. The question arises if Moshe wiped the quill on his hair, why did his face shine?
Or ha'Chayim: This was because, in his humility, he did not want to insert the words "Anav Me'od mi'Kol ha'Adam" (Bamidbar 12:3), so Hashem allowed him to omit the 'Yud' in "Anav". Alternatively - Toras Moshe, Vayikra 1:1, citing Yalkut Reuveni): Moshe wanted to write 'va'Yikar', and not 'va'Yikra', so he wrote a small 'Alef'. (Both of these imply that Moshe wrote the entire Torah on Har Sinai, raising the question why he agreed to send the spies, since he knew the outcome? And why did he err at Mei Merivah, fear Og and Daven to enter Eretz Yisrael ... Perhaps Hashem made him forget these issues. We must say this to resolve Vayikra Rabah 22:1, which states that Moshe received on Sinai everything that every Chacham will teach. Yet he needed to ask about killing the Mekalel, Pesach Sheini and the B'nos Tz'lofchad...! Alternatively, Moshe wrote the Torah only later, and Hashem made his face radiate now, with the ink that he would save later by omitting the 'Vav' or by writing a small 'Alef' - PF)
How is it possible that Moshe did not know that his face was shining?
Oznayim la'Torah: Because initially, he thought that the shine came from the Shechinah, with whom He was speaking when he first received it; then he thought that it was the Luchos that were shining. 1
Oznayim la'Torah: Which explains why the Torah repeats "be'Ridto min ha'Har".
Why did Hashem not inform Moshe of the gift of the Karnei Hod that He had given him?
Shabbos, 10b: Because the obligaqtion to inform the recipient of one's gift 1 only applies where it is not otherwise destined to be revealed, which was not the case here.
How did Moshe merit that his face radiated?
Da'as Zekenim (in Pasuk 30) and Hadar Zekenim (in Pasuk 35), Rosh: Because the people wanted to appoint another leader, so Hashem showed them that there is no-one like Moshe in the entire world.
Hadar Zekenim (in 3:6, citing a Midrash): It is because he hid his face by the burning bush (to avoid looking at the Shechinah). 1
Refer to 34:29:3:5 and note.
As opposed to the opinion which states 'When I wanted [to show you My glory], you did not want. Now that you want, I do not want [to show you]', indicating that Moshe did not merit through hiding his face. See Brachos, 7a.