Happy to take your questions one by one, and I certainly didn't mean to be insulting, not to you, nor to anyone else who has had or will have a genuinely good time at HAND TO GOD. They seem to be in the majority here, which is fine.
I never saw vomit come out of the puppet's mouth that I'm aware of.
I have no problem separating some absolutely wonderful performances by actors from a play that on balance I didn't care for. I adored the subplot about the tough kid in love with his 40-year-old lady puppet instructor-- comedy gold for me. Evil hand puppets interested me much less. For me, the show seemed determined to shock the audience without any deeper meaning behind the shocks, even though it was clear that the creators were convinced there was great profundity there on the nature of Satan, religion and man-made Gods.
As for the comedy, well it definitely took me out of my comfort zone, as it veered from jokes about Texans with funny accents into long sequences about puppet-on-puppet porno (something we'd already seen in AVENUE Q and TEAM AMERICA) and eventually into violence and b-movie horror. The effluvia-stained alley I mentioned was a reference to the copious amounts of blood and bodily fluids depicted onstage. You wrote earlier that you can get mildly squeamish-- there were definitely sequences at HAND TO GOD where I chose to look away from the stage.
Everyone will find a different threshold for what's funny-- what grossed me out (and then bored me) will leave others in hysterics. I'll be eager to see how the show strikes you when you see it.