When is "ba'Eis ha'Hi" referring to?
Rashi: It refers to the end of the second set of forty days, after Hashem pardonned Yisrael on the sin of the Eigel.
Why did Moshe mention the manufacture of the second Luchos?
Ramban and Seforno: To teach us that, in spite of all Moshe's efforts to obtain atonement, so great was the sin of the Eigel ha'Zahav that, although the second Luchos were once again written by Hakadosh-Baruch-Hu, they were made by Moshe, since the people were no longer worthy of Divine Luchos that were made by Hashem. 1
What is the significance of the wooden Aron that Moshe was told to make?
Rashi and Ramban #1: It was a purely wooden Aron with a wooden lid 1 that was to house the second Luchos (and the broken ones - Ramban) until the Mishkan was built, when they were transferred to the Aron that Betzelel made.
Ramban #2: The wooden Aron that Moshe is referring to here is synonymous with the Aron that Betzalel ultimately made 2 - since Moshe was commanded on the Mishkan already before the sin of the Eigel, and the crux of the Mishkan was the Aron, 3 which was the first part of the Mishkan that Hashem commanded Moshe to build. 4
Rashi: It cannot have been the Aron that Betzalel made, since they did not begin building the Mishkan until after Moshe descended with the Luchos on Yom Kipur, and even then, Betzalel first built the Mishkan, and the Aron and the other Keilim only afterwards.
Ramban: In fact, the command to make the Aron is synonymous with the command to build the Mishkan (which preceded the sin of the Golden calf - See R. Chavel's notes).
Ramban: Since the main objective of the Mishkan was to rest His Shechinah - which was to be found in the Aron - among the people. If the Aron mentioned here was meant to house the Luchos until the Mishkan was built, why did Hashem not issue Moshe with the same instructions when Moshe ascended Har Sinai the first time for the first Luchos? See Ramban DH 'Aval ha'Aron', who elaborates in detail.
Ramban: Even though the Aron was made only later, it says here that Moshe made it to put it together with the command to make it, Also see Terumah Sh'mos, 25:10.
How will we reconcile the current Pasuk - which attributes the making of the Aron to Moshe - "Ve'asisa ... Aron", with the Pasuk in Terumah, which ascribes it to the people "Ve'asu Aron ... "?
Yoma, 3b: The Pasuk in Terumah is speaking when Yisrael are sufficiently meritous for the Aron ha'Kodesh to be called after them, 1 whereas the current Pasuk is speaking where they do not. 2
Yoma, 72b: It teaches us that, just as the Aron was made by Betzalel and Ohali'av who were paid by the Tzibur, 3 so too are the Tzibur obligated to support the Talmidei Chachamim who study Torah.
What happened to the wooden Aron after Betzalel built the Aron for the Mishkan?
Ramban: Once the Luchos were transferred to the Aron that Betzalel made, the wooden Aron was hidden.
Seeing as Hashem instructed Moshe to make the wooden Aron after ascending Har Sinai the third time with the Luchos that Moshe made, where did he place the Luchos [whilst making the Aron]?
Rashi: In spite of the order of instructions, Moshe made the Aron before ascending Har Sinai 1
Ramban #1: Hashem meant that he should make a wooden Aron now, in which to place the Luchos when he returned from Har Sinai.
Ramban #2: Refer to 10:1:2:2. Upon his return with the second pair of Luchos, Moshe placed the Luchos in the Ohel Mo'ed until the Mishkan and the Aron were completed. 2
Because even though the instructions to build the Aron are mentioned last, it does not mean that he should make it last. Oznayim la'Torah (in Pasuk 3): And Hashem informed him about the second Luchos first in order to convey to him the good news that He had forgiven Yisrael and would give them a second pair of Luchos, as soon as possible. See there (DH 'Va'a's Aron ... ' #2) also why Moshe took the liberty of changing the order.
Ramban: Which is where the broken Luchos were already lying.
Bearing in mind the sapphire mine that Moshe found in his tent - which he mined to make the Luchos, what was the significance of the shavings that remained from the Luchos?
Refer to Sh'mos, 34:1:2.1:1 and note 1.
What are the connotations of "P'sal Le'cha"? Why did Hashem say it?
Refer to Sh'mos, 34:1:2:1 & 2 and note.
Da'as Zekenim #1, Hadar Zekenim #1 and Rosh #1: In order that the people should not have complaints against Moshe for breaking the Luchos, Hashem ordered him to make new ones. 1
Da'as Zekenim #2: It implies that Hashem was appointing Moshe king, with the power to be Posel (to disqualify) whatever he pleased.
Seforno: It teaches us that, in spite of all Moshe's Tefillos, the second Luchos were made by Moshe, and that they were no substitute for the first ones that were made by Hashem.
According to Sh'mos Rabah (32:1) that the first Luchos brought freedom from the angel of death (people would not die), Moshe's Luchos were no substitute! However, the Gemara in Avodah Zarah 5a and Rashi (in Tehilim 82:6,7) imply that it was lost due to the Chet ha'Eigel; and not to the breaking of the Luchos (PF).
Assuming that the wooden Aron was made to house the second Luchos, why did Hashem not tell Moshe to make an Aron for the first Luchos?
Ramban and Moshav Zekenim: Because he knew that they would be broken due to the sin of the Golden Calf, so there was no need for it.