Yes. However, kaguya is a completionist thus BZ waited for madara to absorb the tree, awaken the rinne sharingan and cast IT first.
The juubi that madara absorbed and the tree are all kaguya besides the power boost I see no difference.
Nope. The shinju contained Kaguyas conciousness at that point. That's why it could talk, and why the Juubi/Gedo Mazo was much less active after Obito was JJ.