What does the expression to deliver a question exactly mean?
Does it just mean to ask a question?
It is unusual, but not wrong. Good writers always try to think of ways of expressing themselves without sounding trite or redundant. You can propose a question, toss one, present one, throw one, shoot one, or almost any other action verb that shows movement from one place to another.
People who are learning English, however, should aviod these creative uses of the language and stick with ask.