If a monster has the Energy Drain special attack, is that a full round action that allows only a single melee or ranged attack per round? Or, if a monster has multiple attacks, can an energy drain occur for each successful melee or ranged attack on the monster's turn?
Well, it depends. There is a 9th level spell Energy Drain, which if it's a spell-like ability would take an action. But usually you're dealing with the special ability Energy Drain, which for a wight, for example, is applied on any attack. You can tell because it says
Melee slam +4 (1d4+1 plus energy drain)
But it's different for different creatures, like the succubus has to grapple someone and then kiss them to drain. In any event, if you read the monster entry closely it will reveal whether it's an attribute of their attack, or a spell-like, or something more complicated.
Anyway, assuming you're talking about the basic undead-critter use case, yes, you can get energy drained with every attack, it takes no extra time beyond the time the attack takes.
"Energy Drain (Su)
Living creatures hit by a vampire’s slam attack (or any other natural weapon the vampire might possess) gain two negative levels. For each negative level bestowed, the vampire gains 5 temporary hit points. A vampire can use its energy drain ability once per round. "
As per rules it can only use its energy drain once per round ... no flurrying monk vampires dropping a lvl 10 character to 0 in a single round. Think you have to check each monster specifically but reckon most of them will be like that