How did Hashem gladden him?
Radak: On Shabbos, You gladdened me when I contemplated Your actions and handiwork (the world and its contents).
Who rejoices and sings?
Radak: Every Chacham. This is why "Simachtani" and "Aranen" are singular.
What is the difference between "Pa'alecha" and "Ma'asei Yadecha"?
Malbim: Ma'aseh is what is finished. While engaging in it, it is called Pe'ulah. The completed creation with natural laws is called Ma'ase Hashem. Pa'alecha refers to Chesed - miraculous conduct via Hashgachah. It rejoices our hearts when we recognize His Hashgachah, reward and punishment. Regarding organized nature, it says "b'Ma'asei Yadecha Aranen."
What is "Aranen"?
Radak: It is [singing] in the heart.
