What are the connotations of "ve'Atah"?
Rashi: Inverting the words "ve'Atah" and "Im", Hashem meant to say that if they would now accept Hashem's authority upon themselves, it would be (relatively) easy from then on - since 'All beginnings are difficult'.
Oznayim la'Torah: Refer to 19:4:2:4. However was a 'free gift' from Hashem, bringing Yisrael to a level they could not possibly have attained by themselves and which cannot possibly last, unless they now work hard on themselves to retain it.
Which covenant is Hashem referring to?
Ramban #1: The covenant that Hashem made with the Avos - "to be for them a G-d and for their children after them". 3
What does "Am Segulah" mean?
Ramban #2 (according to Kabalah): It means 'a nation that clings to Me'. 5
Even though all the nations are favored over and above the rest of the creation (since mankind was the purpose of the creation, as Chazal have said in Avos, 3:18, 'Man is beloved, because he was created in the image of Hashem' - Seforno.
Based on the Pasuk there.
See Rav Chavel's footnotes.
Why did Hashem add "ki Li Kol ha'Aretz"?
Rashi, Ramban and Rashbam: Even though the entire world belongs to Hashem, 1 Hashem chose Yisrael from among all the nations to be His nation (inasmuch as, unlike the other nations, over whom Hashem has designated celestial powers to govern them, He alone governs Yisrael - Ramban). 2
Seforno: (Refer to 19:4:3:1**). One may therefore presume that the pious among the nations are also precious in the eyes of Hashem.
Why does the Torah use the double expression "Im Shamo'a Tishme'u"?
Refer to 15:26:152:1-3.