UK: I’ve got a car / I haven’t got a car
               US: I have a car / I haven’t got a car
 

In British English you can’t omit the word ‘got’ when speaking of possession; therefore you can’t say for example: I have a book/ I haven’t a book.

In certain idiomatic phrases, the word ‘got’ is not used in England, therefore the negative form must be ‘don’t have’.

               UK/US: I have breakfast every day/I don’t have breakfast every day

The I have/I haven’t form is used in England only when the verb ‘ to have ‘ is used as an auxillary (and the same for the US)

               UK/US: I have seen / I haven’t seen

In this case, it would be incorrect to use ‘don’t have ’
 

"shall" vs "will", "should" vs "would"
The traditional rules for using these  are quite intricate, and require some choices. If you're wanting to learn more,  you can access the relevant section of  ‘The King's English’ at:

Very few English-speakers make these distinctions instinctively; most of those who observe them learned them explicitly.
 

When to use "the"
This is often quite tricky for those learning English. The basic rules can be found in the Purdue University Online Writing Lab's WWW page titled "The Use and Non-Use of Articles":
 

and in "An Overview of English Article Usage for Speakers of English as a Second Language" by John R. Kohl of Rensselaer Polytechnic Institute:
 

The article "the" before a noun generally indicates one specific instance of the object named. For example, "I went to the school" refers to one school. (The context should establish which school is meant.) Such examples have the same meaning in all English-speaking countries.