Why does the Pasuk refer to Miri'am as Miriam ha'Nevi'ah?
Rashi: Because she prophesied the birth of Moshe. 1
Rashbam: A prophet is either someone who rebukes or someone who sings praises (of Hashem).
And why does it call her the sister of Aharon?
Rashi #1: Because it was when she was the sister of Aharon, before Moshe was born, that she prophesied.
Rashi #2: Her name is connected to that of Aharon, who was Moser Nefesh on her behalf when she was later stricken with Tzara'as. 1
Ramban #1: Since Moshe and Miriam are mentioned in the Shirah but not Aharon, the Torah wanted him to be mentioned too, so it used the fact that Miriam was his sister to insert it.
And it did so in a way that was a Kavod for him, in that he was Miriam's older sister and that Miriam his sister was a prophetess, seeing as he too, was a Navi and a K'dosh Hashem (Ramban).
What are "Tupim u'Mecholos"?
Rashi (in Eruvin, 3b): It means drums and dances.
Targum Onkelos and Targum Yonasan: It means drums and flutes. 1
Why did the women take musical instruments with them into the desert?
The righteous women of that generation took musical instruments out with them in anticipation of the miracles that they were convinced Hakadosh-Baruch-Hu would perform with them.