How does a masonry fireplace in ICF construction differ from std stick built construction?

Is the firebox and chimney typically placed inside or outside the ICF structure? Is all of the foam removed between the wall and the flue chase to make it fireproof?

there are different possibillities to approach this: You can build an ICF wall around the chimney structure and remove the inside portion of foam after the pour. Or you can stop the ICF wall just short of where the fireplace and chimney starts. The latter is cheaper. A open fireplace structure in itself is a big hole to the outside and therefore provides no energy efficiency when not in use. It is actually exactly the opposite, it will drain energy out of your house - in the winter and in the summer!

Build the entire thing inside the ICF walls. You should have venting for air intake.