Usually on the right lapel.
carnation
wore a red carnation in his lapel for good luck
This is more of a fashion-oriented question. When it comes to politicians, I would say no. Politicians are to wear one lapel pin: the American Flag.
Order of Australia lapel pin. From wiki- “a gold lapel pin for daily wear is issued with each badge of the order at the time of investiture; AK/ADand AC lapel pins feature a citrine central jewel, AO and AM lapel pins have a blue enamelled centre and OAM lapel pins are plain.”
On the left side, always
He wears a US flag lapel pin. Please note that lapel pins do not make one more or less patriotic.
"Tussy Mussy" or "Tussemose" or "Tusmose" are some of names given for the lapel vase that the character of Hercule Poirot wears
across the chest or across the butt
People still wear lapel pins mostly to connect with others in their group. Lapel pins are best worn and used for events to be recognized as a member or participant of something such as a 4th of July parade participant, if you have donated blood, a USA pin and such.
It should be worn over his heart.
"Style" is merely an abstract concept. There are plenty of good quality well, designed lapel pins available. If you find them aesthetically pleasing, wear with pride!