.

In respect to this, what is the difference between Cannot and do not?

The only difference between the two is that "Don't" may be an imperative, while "Can't" is always related to an object. Don't do that versus "You/He/They" can't do that. While don't can state an object as well (you,we,he,she) it doesn't have to be specific, but can be a general directive.

Beside above, can not or Cannot AP style? Can't is a contraction of cannot, and it's best suited for informal writing. In formal writing and where contractions are frowned upon, use cannot. It is possible to write can not, but you generally find it only as part of some other construction, such as “not only . . . but also.”

Subsequently, question is, can not or Cannot?

Both cannot and can not are acceptable spellings, but the first is much more usual. You would use can not when the 'not' forms part of another construction such as 'not only.

Is Can not one word or two?

These two spellings [cannot/can not] are largely interchangeable, but by far the most common is “cannot” and you should probably use it except when you want to be emphatic: “No, you can not wash the dog in the Maytag.” AskOxford: Both cannot and can not are acceptable spellings, but the first is much more usual.