"Too young" to eat karaage? How old is the kid, again? Why would she be too young to eat fried chicken but not too young to eat cupcakes?
Does Japan have a fidelity/trust problem? The trope is way too common, where a partner/potential partner always suspects their love of cheating. It makes sense in a setting where some actions are suspicious, or there's history, but most often it's just a trope without reason.
It's kinda rude not to trust your partner for no reason, it's an intimate relationship and such lack of trust is very unhealthy too.
No, it's because that's just a joke. Like, the reason why these stuff keeps appearing is just because Japanese people like to see them and think it's a funny joke.
This is just a variation of "character gets paranoid and does crazy things but it's actually just all in their head or a misunderstanding", a very common gag. That's it, that's the trope. Cheating is not the point, it's the freaking out over what turns out to be nothing that's the main point of the joke. Like, this is the exact same thing as the kind of misunderstanding gag where someone goes to get food in the middle of the night and then gets attacked because the other people in the house think there's a thief.
Using cheating suspicion as the trigger allows the author to also use "Harmless/timid-looking person goes utterly psycho when angry and pulls out a knife/gun/other scary weapon" yandere gag trope, like in this chapter. Again, also not serious. It's meant to be funny because nothing is happening but the characters are overreacting.