Why did Moshe see fit to 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 manufactured by Moshe, since the people were no longer worthy of Luchos that were Divinely made. 1
What is the significance of the Aron Eitz that Moshe was told to manufacture?
Rashi and Ramban #1: It was a purely wooden Aron with a wooden lid 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 manufactured. 1
Ramban #2: The Aron Eitz that Moshe is referring to here is 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 manufacture. 4
Rashi: In fact, this Aron subsequently accompanied them when they went to war, and on the one occasion that the main Aron was taken to the battle-front, they were punished and the P'lishtim captured it. See Ramban's objection to this explanation. According to Ramban, Moshe's Aron was hidden once the Luchos were transferred to the Aron that Betzalel made.
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.
If Hashem instructed Moshe to make a wooden Aron after ascending Har Sinai the third time with the Luchos that Moshe made, where did he place the Luchos [when making the Aron]?
Rashi: In spite of the order of Hashem's 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.
Because even though the instructions to build the Aron are mentioned last, it does not mean that he should make it last. Rashi - this 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: Which is where the broken Luchos were already lying.
Why does it say "Pesal Lecha"?
Da'as Zekenim #1, Hadar Zekenim #1, Rosh #1: The people should not have complaints against Moshe for breaking the Luchos, therefore he was commanded to make new ones. 1
Da'as Zekenim #2, Hadar Zekenim #2, Rosh #2: The Pesoles (what remains after making them) will be yours. They were of sapphire. Moshe became rich from this!
Da'as Zekenim #3: I am making you king; you can be Posel (disqualify) whatever you want.
Why did Hashem not tell Moshe to make an Aron for the first Luchos?
Moshav Zekenim: He knew that they would be broken due to the Egel, so there was no need for it.