Leash of Oblation questions

You can have Offering of each type. Do I need to cast them myself or they just randomly proc whenever there is corpse around me? Do I need to pay mana for them? Any cool-down on them?

I am trying to upgrade my belt to something more fancy. This one looks interesting.

They still function the same except you can have all 3 at once instead of one.

So you need corpses to consume and you still have to cast/trigger it for the effects. There is no cooldown on casting them yourself but you would have to cast 3 times (once for each offering) and if you use a trigger wand its an 8 second cooldown because the craft says so.