What's the difference between 'half a [noun]' and 'a half [noun]'? Are these structures used interchangeably? 'Half an hour'/'a half hour', 'half a mile'/'a half mile', etc. I'm used to use 'half' as a predeterminer (e.g. 'half an hour'). Can I forget about the second structure altogether?
The difference is small, and you would rarely be wrong to use one in place of the other.
I would probably say a half-thing only if that is a common or natural unit. Many broadcast programs run for a half-hour; you might buy a half-liter of beer. But nobody sells or stores half-apples, so I would say half an apple.