Heimerdinger on hit effects.

Does Heimerdinger's abilities apply on hit effects like Rylai's Crystal Scepter's slow or Morellonomicon's grievous wounds effect? Specifically, do his turrets apply these effects each time the turret attacks or is there a grace period before the effect can be applied again by the turret? Also, do the turrets apply basic attack on hit effects like The Black Cleaver, Frozen Mallet, or Wit's End?