The Immaculate Order still exists, but it is basically what the Christian Church is now. Like how they went from doing crusades and persecuting heretics... to feel-good prayer sermons, doing weddings, and running charities. The Immaculate Order is a shell of its former self. 

Thaumaturgy is still a thing, yes. Though as stated things would be a bit less random due to the dice rolls and other in-game mechanics being gone.

I would welcome someone who is also familiar with Exalted, obviously. Makes my job as a GM a bit easier. So if yiu want to make a monk who is sorta semi-retired and now a doctor/priest, go ahead. Just remember that we are in the Imperial Ruins. And again, they are CALLED Ruins, but the city has become more liveable since it was devastated in the war. Far from what it was, of course. But not an entirely destroyed mess anymore.