Can anyone explain the use of determiners in this passage?

Question 1 - She doesn't need to say "the beans", because it really doesn't matter which beans she's getting. Whether Aki gives her those beans, or some different beans, the question would still be the same. So "the" would be unnecessary. And she could say "some beans", but this would be repeating what Aki had already said. Again, unnecessary.

Question 2 - If she didn't say "the", it would imply that the question related to beans in general ("why beans but not lentils for Setsubun"); but with "the", it really just means "why did you give me those beans".

Question 3 - If the beans that get thrown were the "special holy beans of Setsubia, which are removed from the sacred vial every Setsubun", we might say "we throw the beans". But no, any beans will do; so Aki just says "we throw beans". She could also say "we throw some beans, but not too many", but because she doesn't care about the quantity, she doesn't need to say "some'.

When Lisa asks her first question, she doesn’t use a determiner (or rather she uses what is known as the ‘zero’ article) because she is making a generic reference. The ‘zero’ article is used in this way to describe both plural and uncountable nouns where what is meant is the class of such things as a whole. Aki uses the ‘zero’ article for the same reason.

Lisa uses the definite article when she repeats her question because beans has already been mentioned. The definite article is used when both speaker and listener know what is being referred to and beans has already been mentioned in the conversation. (However, Lisa could just as well have used the ‘zero’ article as well for the same reason that it’s used in the other two sentences.)

If you find this confusing, you’re not alone. Non-native speakers of English whose own languages have no articles nearly always find them difficult.