oughtn’t (to) do

English as a Second Language English Vocabulary, Grammar and Idioms
1

We know that after the modal ought we use the infinitive with to.
And this makes ought different from other modal auxiliary verbs:
You ought to see a dentist.

 However, in one of the well-known American English grammar books

the following definition is given:
Ought to is not commonly used in the negative. If it is used in the negative,
the to is sometimes dropped:

  You [b]oughtn't (to) leave[/b] your keys in the car.

Dear Teacher! I have not met this kind of rule anywhere, so I have three questions

regarding this subject:

  1. If it is true, does this rule apply only to contracted form of ought not ?
  2. Is there any difference between AmE and BrE (not in vain am I asking this question since this rule has been taken from an American English Grammar Book)?
  3. Also, any difference between formal and informal language?

Could you please answer all the three questions?

Respectfully.

2

My question has remained unanswered for two days.
Did I ask a diffucult question?
Could anybody specialised in English Grammar answer this?

3

In my (BrE) experience:

oughtn’t to (or ‘ought not to’, as the same applies to the full form)… is not often used, but where it is used, I think the ‘to’ is kept more often than it is dropped.
The obvious difference between the formal and the informal is that in informal usage the contraction is more likely to be used.

4

Above all, thanks for answerIng my question.
In the following sentence grammar and semantics/word choice is OK:

My question has remained unanswered for two days.
5

Yes, that’s fine.