Could be. I think it's more to do with the fact that Pazuzu wanted the soul of the priest (for various reasons), and the whole thing was a set-up so that he could eventually possess said priest (the younger one. The older one also dies, so I guess that's a double success, from Pazuzu's standpoint)...
Technically, no...
It's Pazuzu, an ancient Mesopotamian wind demon (hence the beginning of the movie)...
Which is partly why it is not actually affected by holy water (if you watch the movie closely).
It's... Complicated. But it's not Satan she is possessed by, no.
It's never fully explained why the Catholic rituals "work" (or, at least, appear to) on said demon, but yeah...
power of belief in god, maybe?
Could be. I think it's more to do with the fact that Pazuzu wanted the soul of the priest (for various reasons), and the whole thing was a set-up so that he could eventually possess said priest (the younger one. The older one also dies, so I guess that's a double success, from Pazuzu's standpoint)...
That's one interpretation, anyway!
But possibly also what you say there, yeah...