The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
^ I think Not in Front of the Kid is for in-universe cases, what OP is describing sounds more like a trivia trope.
As for the second, maybe Children Are Innocent? That definitely doesn't apply to South Park though.
I do some cleanup and then I enjoy shows you probably think are cringe.
^ I think Children Are Innocent does fit in the South Park example, since those episodes are based on the Ping Pong Naivite of the kids. It's the closest thing I've found, at least.
But you're right about item 1. I'm looking for tropes related to editing tricks such as Fake Shemp.
1 - When a movie that features rauchy humor or extreme gore has a child actor, scenes are often edited so that the kid isn't present during the recording of the dirty/violent scenes, because the crew is worried about the kid's psychological balance. Some movies make a point of showing the editing so viewers can relax knowing the innocent little actor wasn't subjected to graphic images. (for example, that scene from Clerks where Randall is listing off a bunch of porn movies he needs to buy, and a lady with a baby is hearing it with a shocked expression). What trope would that be?
2 - Some works (or some episodes of a certain work) feature kids in a realistic setting that celebrates the bittersweet innocence of childhood, as opposed to setting the kids up as wiser than their elders, sarcastic, competent, mature, or involved in speculativeFiction tropes. I'm thinking in particular of the "kids being kids" episodes of South Parklike "Return of the Fellowship of the Ring to the Two Towers". Is there a trope for that?