Orochimaru was healthy actually. He could make seals and everything. The only time he was sick is when Hiruzen used the Reaper Death Seal on him, THAT'S what made him sick. This took place before that. He was trying to steal his Sharingan, whether he was dead or alive, not his body.
Orochimaru was trying to take Itachi's body, just like he tried to take Sasuke's; Sasuke confirmed this. If he just wanted the Sharingan, he could had plucked them from Sasuke at any point.
Orochimaru was trying to become the next Rikudou, he wanted Itachi's/Sasuke's body and was experimenting with Senju cells. Kabuto confirmed this.
Orochimaru can only trade bodies once every couple years when his host starts to reject him, he's dying and weakened. Orochimaru had to leave his fight with KN4 because his body started to give out on him, and he had to take Genyuumaru's body because he couldn't wait for Sasuke any longer or else he'd die.
And even then, Itachi didn't "beat" Orochimaru, merely forced him to back off. Orochimaru is an immortal regenerating freak, getting shopped to pieces makes him giggle, so losing a hand literally meant nothing. So no, he couldn't take Itachi's body so he had to go find another one before he died.
He also lacked killing intent, something Itachi also lacked against Sasuke so don't be a hypocrite.
In the battle against Sasuke while he was purposely losing as well as dying from a terminal illness, he used Tsukuyomi, spammed Amaterasu, and used Susano'o. I'm sure he has enough eye durability to do it.
Nagato could walk in that battle, he wasn't immobile, so I think that it is actually fair.
You're right. Amaterasu isn't instant. But the only person I remember dodging it was Ay, and his speed was on par with the likes of Minato and KM Naruto. I don't see Oro moving that fast, or responding that fast. 50 meters isn't as much as you think it is. Even Obito couldn't respond fast enough to dodge the Amaterasu. He had to use Izanagi in order to escape it.
That would be impressive if Sasuke were more powerful, but he was still weaker than armless Orochimaru and proceeded to get his arrogant hide smacked around by the Gokage.
Itachi purposely losing also renders any negative effects from his "illness" moot, since he was trying to take a dive. Besides, Itachi was dying from Susanoo, that was his illness.
Itachi used Tsukiyomi, activated Susanoo twice, and used 2 Amaterasus.
Nagato's legs were still impaired and Kabuto said that's why Nagato was hit by Totsuka.
How many people has Amaterasu been used against? lol. Sasuke dodged Amaterasu. Obito was hit by Amaterasu from 50 meters away? No. Just so you're aware, 50 meters is 164 feet. Gyuuki wasn't even that far away from Sasuke and he still intercepted it with his tail.