Of course sneezing is a violation of the Prime Directive. You're contaminating their ecosystem with your alien germs!
To the Emissary role... yes you said it yourself he discouraged it... at first. Later he didn't and fully embraced it. That's text book interference.
The Tosk incident wasn't a violation because he let him on the station. It was interference when Sisko underhandedly help O'brien break Tosk out so the Hunters wouldn't get him.
ITPM was textbook internal interference. It doesn't matter that they had prior conflicts with the Dominion, they weren't a part of the war at that point, and Sisko and Garak underhandedly manipulated the Romulan political system to force the Romulan Star Empire to enter the war. Garak took it a step further but that was what Sisko was setting out to do from the teaser of that episode. If that's not internal interference, what is?