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'.
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 who cleaves 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 notes.
Why did Hashem add "ki Li Kol ha'Aretz"?
Rashi and Rashbam: Even though the entire world belongs to Hashem, 1 Hashem chose Yisrael from among all the nations to be His nation.
Ramban: although the entire world belongs to Hashem, He chose Yisrael to be His - inasmuch as, unlike the other nations, over whom Hashem has designated celestial powers to govern them, He alone governs Yisrael. 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.