1)
Why is Devorah mentioned first?
1.
Radak: She was primary. Similarly, "va'Tdaber Miryam v'Aharon" (Bamidbar 12:1).
2)
Why is the Shirah attributed also to Barak?
1.
Tana d'Vei Eliyahu Rabah (10): He trusted in Elokei Yisrael and in Devorah's prophecy.