What is the difference between Shamayim and Shmei ha'Shamayim?
Ibn Ezra: Shamayim is the Raki'a. Shmei ha'Shamayim are the higher spheres (on which the Heavenly bodies rotate).
What is the significance of the matters mentioned in this verse?
Malbim: Via three matters Hashem is known to His creations. (a) The creation - He created upper and lower beings. (b) Sustaining the creation and constant conduct - "Atah Mechayeh Es Kulam." He is unlike other workers, that after they made something, it lasts by itself. The entire creation endures only because Your are the Nefesh that gives life to it, even though it looks like the conduct is via Tzeva ha'Shamayim and the Ma'arachah, they bow to You - You conduct them, give to them strength and rule over all of them. (c) Refer to 9:7:1:1.
