All kinds of Ninjutsu were developed after Kaguya's time.
Although I suppose all KKG came from her. All we know is that Hagoromo spread her chakra throughout the world. Perhaps those who were lucky acquired fragments of her power (KKG) in addition to the chakra that they had gained. In time, they came together and formed their clans.
That's how I believe it happened although it's just a hypothesis.
Perhaps she was able to use all KKG. We wouldn't know since Kishi kishi'd her up.
Yup, I blame it on the writer. That fight.and Kaguya's character could've been SO much better.