How so? It's not about paying respects. Just normal respect that one should show towards all (good) people.
Yes. "dzieci" is a bit illogical, true. But the singular form "dziecko" is neuter, and even if those specific children that you are talking about are boys only, still it's "one" as you decided to go with the word "dzieci" and not "chłopcy".
"ludzie" is logical, because by definition this should include at least one man (otherwise you go with "women") so it's masculine-personal.
I do not understand why the sentence is not in Genitive case, like "ona szanuje mojego wujka".
None of those is Genitive. "szanować" takes Accusative.
"uncle" is masculine, and as it denotes a person, it's also animate. Accusative of masculine nouns is the only situation where it matters whether the noun is animate or not. Animate ones have Accusative identical to Genitive. The inanimate ones have Accusative identical to Nominative.
For 'not masculine-personal plural', the Accusative form is identical to Nominative.
Do Polish people talk about respect more than English speakers? It seems a strange thing to say.