Kagome must clearly have some insight into things. She took Shippou's father's pelt though she was rushing after Shippou; maybe some little part of Kagome sensed something with it,
unconsciously taking it with her.
It worked, yes.

Remember how Manten disappeared? I suppose it happened with the force of the Shikon shards and his vengeance. Seems those little spirit shards could have some play in that,
turning his state into a spirit one.

And, a  little insight into our boy:
His sword skill is improving; yes, and he is not alone anymore.
Nope, now he has a l'il kitsune joining in his travels.
He is not some claw-slashing crazy; he looked out for Shippou.
He is not so much into revealing emotions to people, but sure looks like that lone fortress within him is slowly dissolving. He has Kagome; her personality just might fill up his empty spot to make him whole. He's got Shippou, a little fox demon to pick on like a little brother.
And, when Myouga's around, he has someone knowledgeable.
His friends are picking up!

Shippou, Shippou! A loyal fox cub, strong and determined. Interesting array of illusions he's got there.