The angels and demons in the series are ethereal beings with (ethereal) wings, and angels can take physical form to make themselves look human, but with wings. Both angels and demons can fly in their ethereal state, and angels can fly in their physical form as well.
Demons lost both their ability to assume physical form and their physical/angelic beauty when they lost the War in Heaven, which many (most?) Catholics believe happened at the dawn of Creation. Augustine believed the separation occurred when God separated the day from the night in Genesis, a metaphor for good and evil.
Demons in physical form are the corporeals, which are dead human bodies, so whatever a living human can do in the story, a corporeal can do too, which excludes walking on water, which is a trick only Connor can do. Corporeals are generally much stronger than humans and perhaps faster (I haven't decided their speed yet). The only time demons in a physical form can fly is if they possess a (non-human) animal that can fly (e.g., the demonic locusts Connor fights at the Sea of Galilee during the prologue, and the demonic birds that attack their vehicle on the road in Israel).
My demons don't heal the sick. But they can heal signs of decay in the dead carcasses they wear as bodies. Also, for corporeals to work in the story, they can access/inherit the memories of the dead hosts if they get to the bodies quickly enough (before the brain cells die).
To ensure consistency across the trilogy, I had to make it that demons can modify the bodies they inhabit. In the case of human bodies, they modify the bodies to "heal" limited signs of rot in corpses; in the locusts, they are able to create scorpion-like stingers at the back of locust bodies. I suspect the author of Revelation didn't intend for demonic locusts to be demon-possessed living locusts with modified tails, but it avoided a big inconsistency of having demons be able to assume the physical forms of lower animals but not the physical form of humans, hence they can "modify" whatever creature they inhabit, rather than changing themselves from ethereal into physical form directly.
Given how severe the corporeal bishop's reaction to swallowing holy water was, it should cause something far more severe than itching, even in De Rosa. However, I don't yet take advantage of the fact that even Satan is at least somewhat susceptible to holy water. In early version of the book's first draft, I had something similar to itching for De Rosa's reaction to that Christian chain locked around his neck, but readers knew almost immediately that he was a likely bad guy. So, I modified the effect of the chain to cause him stigmata pain/wounds whenever he murders one of the cardinals.
For what it's worth, demons cannot kill the pope, not even Satan. It would be too painful to try since he is the Vicar of Christ (he's protected from demons by God). That's where Connor comes in. Satan uses Connor to try to kill the pope, although the little demon-spawn couldn't go through with it when the time came.
While the chain in Revelation does seem big from a literal reading, Catholics view much of Revelation as figurative anyway. It therefore seemed reasonable (and convenient!) for me to define that chain to be a simple necklace with a Christian cross on it that Satan cannot remove and that causes him painful wounds to reflect the murders he commits in the book. A supernatural necklace with a cross is, in my mind, more powerful than any physical chain. In the final scenes involving Satan and his demons in the trilogy, they're all teleported to an asteroid, and all have Christian crosses secured around their corporeal necks, preventing the demons from escaping their dead host bodies and the asteroid as it spirals into the black hole.
Many Catholics interpret Revelation to be a spiritual story more so than a simple physical one, including the idea that there is no physical massing for a battle against Christ on Armageddon either. It's the reason, my final battle of the trilogy will be Satan's forces against Connor's forces, ultimately interrupted by Christ's return, not Satan and Connor against Christ. God the Father gives the angels the option to fight for Connor, which some of them do, led by Michael the Archangel.