Wouldn't more natural translations would be "I have some small apples" or "I have got some small apples?" "I have small apples" is grammatically correct, but (at least in the UK) its like saying I have small apples as part of my body, rather than I possess some small apples.
No. The verb "mieć" (to have) requires noun in Accusative. Just the Accusative case of "jabłko" is the same as Nominative.
What is written means I have, but the man said mamy which means we have.
Yes, I agree... the only thing I can do about it is disabling the audio exercises, so no one gets the 'type what you hear' exercise.
That would be a shame if it means disabling a whole lot of listening exercises. They are so valuable. Maybe just leave as it is?
Well, an exercise which you fail (because the answer is "Mam") despite the fact that you correctly wrote what was said ("Mamy") is hardly valuable, on the contrary.
Luckily, it's the first such problem that I encounter with the new voice.