Is she a bokukko?
Not really, she uses "jibun" to address herself. She sounds quite manly to me, but I think mostly is due her Okinawan accent..
What other male qualities does Hibiki possess?
Good at sports, fighting spirit... tomboyish like Makoto, perhaps, but Hibiki is not popular with girls.
What's the reason behind Hibiki being boy-ish?
I think is because she was raised with boys. At least, she have an older brother, and their relation is similar to the love-hate (sort of) relation with the Producer.
Is her liking pets a sign of her femininity or masculinity?
At first she wants to take Yayoi home because is cute, so I think is a femininity sign.