If I play a troll vomit with numberless grave! and i destroy 3 opponent's unit. How may cards have I to draw? One or three? Does each destroyed unit trigger the grave's ability?

You *may* draw as many cards as there were units destroyed (its an action, so its optional). This card is not like Garden of Morr, which says "when one or more units are destroyed". It behaves more like Glittering Tower, triggered once for each time the event (unit destroyed) occurs.