All of these expressions are completely acceptable.
- Could I have half a pound of butter? / Could I have a half pound of butter?
- I waited for half an hour.
- The dog eats a half pound of hamburger every day. / The dog eats half a pound of ….
Note the expression ‘a half bottle’. This is used to refer to a half-sized bottle of wine or spirits.
Avoid expressions like a half a and a half an.
- He had half an orange. / He had a half orange. (BUT NOT He had a half an orange.)
You can learn more about half here.