Use contractions whenever you can -- it sounds more natural. Use the 'long form' 'it is not' for emphasis when you want to stress something. Normal speech: It's not ok to cheat on the test. Stressed speech: It is NOT ok to cheat on the test!!

The only real difference between these two is when you mean for the "not" to apply to something else, in which case you would say "it's not" to keep the "not" separate. For example: "It's not doing you work that got you into this trouble." The "not" here is applying to doing specifically, so it can't be combined with "is". Other than that, there's no real difference.

No it's only an abbreviation.