A girl has no name
I was waiting for someone to reference that since in so many of these lessons, the answer is something like "A boy sees an animal"
Why chłopiec and not chłopca?
Because "a boy" is the subject of the sentence, so it takes Nominative.
Compare with "A boy hears a boy": "Chłopiec słyszy chłopca".
Chlopiec vs Chlopak?
Young boy vs an older boy. Very subjective, no clear border in age. I wouldn't give "chłopiec" more than 12-13, personally.
"chłopak" can also mean "boyfriend" - if it's "someone's chłopak", of course.
Would tę work here or is that a bit more of a definite article thing?
On its own it would be fine, but that's "A boy hears this woman" (or it's an acceptable interpretation of "A boy hears the woman").
Блин а че słyszy, а не słysze
Is 'kobietę' the accusative case?
Yes, it is.