Well I assume inside of Kamui Obito is in charge much like Madara was when he brought Obito into his genjitsu world via mazou
Not really. It is not "Obito's dimension", it's only an alternate dimension that Obito has access to. So does Kakashi, neither of them are in charge there.
errr we don't know that.
Confirmed? Was it ever, realistically, in doubt?
You'd have to ignore the 7 pages before the 'Hole' if you thought it wasn't genjutsu. The biggest problem with the manga is that people don't pay attention.