The unhelpful answer is “whenever people realize something “special” might be going on”, probably around the sixth or so. You could make the case that increasingly up-to-the-minute coverage (new leads on the MLB home page, etc.) has gradually pushed this time earlier.

As far as performance being helped by normal dugout environments, I would say that the isolation is probably more likely to make a pitcher “snap” a little. But it could also more likely to keep him sublime–normal dugouts produce normal results, abnormal dugouts produce abnormal results? You just don’t know which one it would be…

Complete isolation while a no-hitter in progress is a superstition(ritual?) I’ve never completely understood. During what inning do other teammates completely stop talking to the starting pitcher? What do the un-written rules say? The 5th, 6th, 7th? During that 5 or 6 pitcher combined no-hitter magic trick the Astros performed a few years ago against the Yanks did each of those pitchers still receive the “treatment” in the dugout?

I’ve noticed that the starting pitcher usually isn’t talking to many people early in the game anyway, but does the poor guy need a 15 foot buffer on the bench later in game if his no-hitter is still intact? I would argue that he would perform better if he was still exposed to a normal dugout environment. God forbid if someone made a joke about his streak being snapped to loosen him up for the next inning!

Well Math, I hate to break this to you, but you’ll never completely extinguish my superstitious flame. <- Very well put.

Taking the discussion points out of order:

Is baseball the sport where you find you’re the most superstitious? Yes. It's also the only one I regularly follow on a professional level. Make of that what you will.
What are some of your favorite superstitious rituals? Not mentioning perfect games or no-hitters when they're in progress. Other than that, I don't have any favored ritual actions per se, but rather feel that consciously paying attention is helpful.
How superstitious are you while following your favorite team? The no-hitter taboo applies for any team. As far as rooting goes, it's less "superstitious ritual" as much as "delusions of grandeur".

Harry's questions: I employ a complex, multi-level doublethink when dealing with baseball. While I happen to be one of those people who do profess belief in a Greater Spirit that can affect the world as we know it, I'm generally leery about invoking it for selfish reasons/disdainful of those who would do so. The trickier belief to justify is that in a not-as-great force that converts psychological states to mundane actions in the real world. Try as I might, when it comes down to it, I can't deny that I believe in the latter, /too/.

…that was unnecessarily philosophical, sorry, but if you're not sick of my ranting by now my opinions are essentially summed up by http://humbug.baseballtoaster.com/archives/1085362.html.