Depends on the sentence. Either 1 or 3 could be right. 2 is always wrong. Examples: I'll do it in half an hour. I'll do it on the half-hour. It is a two and a half hour job.

half an hour

1 and 3 are fine.

The only one which is wrong is number 2. 'Hour' begins with a silent 'h', so you can never say 'half a hour' You can say 'half an hour' (1) and you can also say 'a half hour', which would make number 3 right. For example: I booked a half hour session with my physiotherapist.

Half an hour) is the correct one coz of "h" is silent here.