How much a political leader smiles reflects their particular country's cultural values related to how people express themselves, Stanford research shows. The more a particular country's culture values excitement, the more its political leaders show enthusiastic smiles. On the other hand, when the specific culture emphasizes calm, those leaders show more reserved smiles. In the United States, the smiles of politicians and other leaders tend to be big and wide. In East Asian countries like China and Taiwan, they are much more modest. http://news.stanford.edu/news/2016/february/smiles-jeanne-tsai-021516.html
There are expression trainers to teach VIPs how to smile ... and they sure practise this. I have no good source for this claim, but an story: http://www.globaltimes.cn/content/732019.shtml Body language is just another language. People use this to communicate as they use words, and of course all sorts of treachery and lies are told by body language as well a in words.
Our smiles are derived from a aggressive guesture in animal kingdom - showing teeth is a threat usually. (And that's why it's better to smile with closed lips when facing an animal which you want to befriend). I have no idea why we humans smile to express positive emotions which include the opposite. It originally was just saying "I am stronger/more dangerous/superior/don't mess with me". So if you say it still works that way in your culture, you're just closer to the orgin. Teeth were a weapon. Showing teeth was a threat.
Exactly. Showing your teeth to certain animals, no matter if you just smile, might not end well. Showing teeth is always a threat in animal world. Might have been connected to the culture of human smile.