Negative questions are of two kinds: contracted and uncontracted. They have different word order. Note that uncontracted negative questions are usually formal.

Contracted negative questions

Form: auxiliary verb + n’t + subject
Didn’t she come?
Don’t you understand?
Weren’t you surprised?

Uncontracted negative questions

Auxiliary verb + subject + not

Did she not come?
Do you not understand?
Were you not surprised?

Non-auxiliary have and non-auxiliary be can begin negative questions.

She hasn’t any friends to help her. (negative statement – formal GB)
Hasn’t she any friends to help her? (contracted negative question)
OR Doesn’t she have any friends to help her?

She is not at home. (negative statement)
Is she not at home? (Uncontracted negative question)
Isn’t she at home? (Contracted negative question)

Two meanings

Negative questions can have two different kinds of meaning. For example, a negative question can ask for confirmation of a positive belief. In this case it expects the answer ‘yes’.

Isn’t it true that she is going out with an old man? (I believe that she is going out with an old man. Now I am just asking for confirmation.)

A negative question can also ask for confirmation of a negative belief. In this case it expects the answer ‘no’.

Aren’t they coming? (= Am I right in thinking that they aren’t coming?)

Note that the meaning of a negative question is usually clear from the context and situation.