"I am buying half of the apples."
Translation:Kupuję połowę jabłek.
"pół" is more like the numeral 0,5. It doesn't really make sense with a plural noun. You can have "pół jabłka", "pół kilograma jabłek", but not "pół jabłek".
Granted, 'half of the apples' isn't the most intuitive thing to say... but as I wrote in another comment, it's like "half of the apples they had".
I know this doesn't make much sense but what if someone would sell half-apples? Like: I bought 6 half-apples. Would there work "pół jabłek"?
Yes, you use "kupować" with Accusative.
połowa [Nominative] -> połowę [Accusative].
Half of the apples (they had in the shop, for example), not half of one apple.