In the United States we do not say "half nine". We'd say "half PAST nine" sometimes but honestly "nine thirty" is a lot more common.
Same thing in German though. Usually you only use "drei viertel neun" and "halb neun" (i.e. 8:45 == three quarters nine, and 8:30) but in some regions they say "viertel neun" (quarter nine) for 8:15, but the people not from that region often mishear it as "viertel nach neun" (quarter past nine) because why would you say the former, so the speaker must have spoke the 'nach' too silent...