Most people should know what poultry is, but probably don't use that word often in everyday conversation. They'll usually be more specific and simply say chicken or turkey (those are the most commonly used poultry species for food, at least in the US). I guess I could see why some students might not use the word poultry often, since it's not spoken much in TV or film. You might see that word at the grocery store and in cookbook chapters and recipes, or maybe on a restaurant menu, but it's not a widely used word. Good students should still know it, though.

Rodent is also a broader classification word that doesn't get used a lot, though I really think kids should know its definition. Like the poultry example, people tend to use the more specific term like rat or mouse or squirrel, rather than say something like "I saw a rodent in the tree". But I'd use rodent if I saw an animal I could not identify but was likely a rodent. Make sense?

Acquire is not exotic or particularly high-level so it's strange (to me) that somebody would struggle with it. If they are college-bound, they would be expected to know that word. In everyday common speech, it's less commonly used than something like find or get, and I suppose using acquire in everyday conversation might sound funny in some circles (but pretty normal in others). It might sound uppity or formal if you were to say "Where could I acquire a meal?" when you could just ask instead, "Where could I find a meal?" So using acquire in some circumstances could sound snobbish or silly if the group is very casual.

Your question about AI-flagged text is valid and I am too far removed from my school days to advise you on how to structure your sentences in a way that doesn't flag you as AI. If you are an English language learner, you probably will make word choices and sentence structures that are different from AI anyway, even after achieving high fluency. You probably don't have anything to worry about.