Itachi's Genjutsu will work on Kakashi. Breaking it and getting caught in it are two different things. By the time Kakashi breaks it Itachi would of already converged upon Kakashi's location, and once that happens Kakashi won't be able to use Kamui. He even stated he can't use Kamui up close. Or Itachi can simply put him in it and then prep an H.I. to use against Kakashi. If he breaks the Genjutsu in the time before H.I. is activated, it's still too late; it takes 1-3 seconds tops to activate. Kakashi wouldn't be able to react in time especially since he doesn't know that Itachi is even using it. Nagato could distract Jiraiya via ST so he cannot defend Kakashi.
As for Gama Rinsho? Like Centurion said, sound Genjutsu has already canonically countered by basic Fuuton.
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Nagato has Fuuton. In fact, he mastered it beyond normal means because of his possession of the Rinnegan.
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