1) ✖️He drank half glass of milk
✔️He drank half a glass of milk
Half a glass (а также an hour, a day, a mile и тд) это сокращенная форма от half of a glass. Поэтому a нужно сохранить.
2) ✖️ I paid six pound for the book
✔️I paid six pounds for the books
(тут, видимо, злую шутку играют выражения типа three hundred, two thousand и тому подобное)
3)✖️I told them not to make noise.
✔️I told them not to make a noise.
То же самое касается: to make a mistake, to make a fortune, to make a will, to make an impression, to make an experiment, to make an attempt
4)✖️Can you supply me all I need?
✔️Can you supply me with all I need?
И точно так же: He provided his son with all he needed