There is a distinction in english between 'the half something' and 'half of the something'. In the first instance there only ever was half of the thing (e.g. someone made a half-size wall, or a half portion of breakfast), whereas in the second instance there was originally a whole something, and now there is half.
I ate the half breakfast : a half-portion of breakfast was there and I ate it.
I ate half of the breakfast : a full breakfast was there and I ate half of it.
We built a half wall : a half size wall was built - job done.
We built half of the wall : half of the wall is built but we have still to build the other half
From what I can see there appears to be no such distinction in Greek
I can't check the slow audio but on its own page έφαγα is not clear, as you say. It actually sounds good on the standard speed audio in this sentence. When you want to check the pronunciation of a word individually I suggest using forvo.com or el.thefreedictionary.com. For full phrases you can use acapela-group.com.