The script describes these handles as "ornate brass levers". These release the blood sacrifices that are being offered to the 'old one' in order to placate him.
Based on a Q&A with the film's director, We can confirm that they're releasing human blood
"Yes. Sacrificial human blood"
but there's no indication where this blood came from originally. Given the extreme level of access the staff have had to the lives of their victims (as evidenced by their ability to compare Jules' blood-work to earlier levels) there's at least a possibility that this is the blood of the victims, harvested for the purpose.
Sitterson : This [the blood] we offer in humility and fear, for the blessed peace of your eternal slumber, as it ever was
Presumably in olden times this would have been accomplished by sacrificing their victims directly over the altar, something that's harder to accomplish with the present set-up, with the risk of their blood being destroyed or impossible to extract.
With regard to your second point, the ground shakes violently when the Fool's handle is triggered prematurely. It seems that the gods do have an issue with being offered the blood of a sacrifice who hasn't suffered and died appropriately.
CLOSE ON A LEVER as a hand pulls it down -- CH-CHUNK- -
...Suddenly the rumbling fills the room, which starts to shake with what
feels like a decent-sized earthquake...
...Hadley, Sitterson and Truman all pause to look around as they too are
From a production perspective, the obvious metaphorical connotations of the "people behind the scenes pulling levers" shouldn't be too hard to work out.