What were the ornaments that the people did not put on?
Rashi and Targum Yonasan: They were the holy crowns with which Yisrael were adorned when they declared "Na'aseh ve'Nishma!" (on which Hashem's Holy Name was engraved - Targum Yonasan). 1
Ramban #1 (in Pasuk 6) and Rashbam: Hashem simply meant that since they were in mourning, they should not wear the ornaments that they received at Har Sinai.
Ramban #2 (in Pasuk 6, citing Targum Onkelos): They were the 'weapons' 2 that Yisrael received at Har Sinai - to protect them from all harm and from the Mal'ach ha'Maves. 3
Da'as Zekenim #1: They were their weapons - which they refused to gird in order to go and fight (against the Cana'anim) unless Hashem accompanied them.
Da'as Zekenim #2 (citing R. Yosef Karo): They were the nice ornaments and prized clothing that they wore at the time of Matan Torah.
Oznayim la'Torah: They were their ornaments of silver and gold, which, of their own accord, they did put on, in order to atone for having having taken off their golden earrings for the Eigel. 4
And which were removed when they worshipped the Eigel. Refer to 32:25:2:6* and to 33:6:151:2 and note.
Ramban (in Pasuk 6: Comprising Names of Hashem (Ramban, Pasuk 6).
In other words, they now accepted upon themselves death - a great source of Teshuvah.
Oznayim la'Torah: And are not to be confused with the ornaments that they receoved at Har Chorev in Pasuk 6, which they did not take off until Hashem told them to (in Pasuk 5). See Oznayim la'Torah who elaborates.
What was the "evil matter" that they heard?
Rashi and . Moshav Zekenim (in Pasuk 3) #1: It refers to the Shechinah not accompanying them.
Moshav Zekenim (in Pasuk 3) #2: They heard that the angel would expel the Cana'ani nations, but would apparently not remain to help them afterwards.
What did their mourning achieve?
Moshav Zekenim (in Pasuk 3): Hashem, in His mercy, saw the mourning, and called them by their cherished name, "B'nei Yisrael". 1 He also explained to them that it is for their own good that He would not go with them.
Whereas until now, he called them "Amcha" or "ha'Am".
QUESTIONS ON RASHI
Rashi writes that "Edyam" are the crowns that Yisrael received when they declared "Na'aseh ve'Nishma." But angels came and removed them after the sin of the Eigel?
