I don't think he's in Hashi's. His chakra is pretty melded with the Juubi's turning it into the Juubi's usage of Nature Energy, which is technically Sage Mode, but also not a Sage Mode.
Logically no. He stole the sage mode from hashriama, so presumably he has a set amount as he can't absorb it himself. All the tech's he's used as Juubi jinchuriki should have drained it out.
I think so but I'm a bit confused. Being the ten tails jinchuuriki already gives one access to nature energy yet presumably he's still in hashi's sm.....