I highly doubt that when Obito said "luckily I could keep some secrets hidden...even from him" that he was referring to kamui. 3 members were confirmed to have known about it, including Deidara, Konan, and Nagato. If he used it freely in front of those 3, why not the others? He probably knew about it. It looked like Obito used Izanagi to get rid of that amaterasu activation. He was screaming and in pain, then in another panel we see him completely fine and his clothes aren't damaged.
As for Itachi thinking Tobi was Madara, that's not really his fault here. Everyone in the world was fooled. Though, he did obviously have his suspicions considering that he stated, "But know Madara is just a shell of his former self and not worthy". It looked like Obito wasn't fitting the expectations that Itachi had, considering that Itachi himself did read about Madara. However, in a world where it's possible for immortals to exist, it's not that hard to believe that Madara stuck around. Also, Itachi had no way of knowing that it was Obito...considering that Obito was 9 years older than him. Obito disappeared from Konoha when Itachi was 4, they had never met before the Uchiha massacre. How can you know someone's true identity, when you never met their true self in the first place?
And as for what Itachi said about Obito/Tobi "Madara" being his teacher, that was a lie so that he could tell Sasuke the story behind Madara and the EMS, so that way Sasuke would know what to do after going blind himself and take his eyes. He had to give an explanation as to how he knew Tobi. He also expected Sasuke to get strong enough to defeat Tobi, and become even more of a hero, so Itachi had to give an excuse as to how he was affiliated with him. By telling Sasuke about Tobi, it allowed for Sasuke to go after a new target and for Sasuke to know the secrets behind EMS. The funny thing is that Itachi told nearly not a single truth since the moment he left Konoha...and didn't reveal it until he was an Edo.