It does bother me that her fan switches hands and randomly disappears. I wish she'd just keep it in her right hand at all times like Bankotsubo did.
In regards to the random wind effects, I've noticed that they specifically seem to float around her fan when it teleports from hand to hand, and she has specific attacks that will warp the fan to whichever hand will be closest to the foe after the attack it complete.
As for throws and OHs, I've notice the fan disappear completely during 66T, and if you are in training and reset position while doing 66T, the fan will be gone completely, until you attack again. In addition, I've also noticed that fan will warp to her other hand during her air throw, if she was initially holding it in the hand that she grabs the foe with.