Even in very informal letters, "gonna" and "wanna" seem strange to me, as if the writer is trying very hard to seem "cool". It may give the wrong impression. To be on the safe side, stick to "going to" and "want to".
Using idioms like "spill the beans" in an exam should impress the examiners, if they know what the idioms mean. Don't use very new idioms from the world of rap and hip-hop; examiners may not understand them, as they belong to a very small community. That includes "hit me back", "holla back" and "fo'shizzle". Even in real life, if you are ever in New York, don't use phrases like this unless you are an expert in their use -- you'll sound foolish if you try and get it wrong.