Three action senses, all on shān (first tone). Literal:
扇风 (fan the air). Slap:
扇耳光 /
扇巴掌 (slap across the face) — the motion mirrors fanning. Incite:
扇动 (to flap, but also figuratively to stir up trouble),
扇风点火 (literally 'fan wind, kindle fire' — to instigate). The noun reading
扇 (fan, door-leaf, classifier) handles everything else.