I don't know how else to state my question. What I'm looking to do seems like it ought to be very simple.
I want to take a brand new torus, and cut it in half. i.e. the exact shape you'd get if you cut a real donut in half (with the sliced edges being a face (I don't care if there are multiple edges / faces).
The same thing, but only cutting out 1/4, i.e. removing the bits of the torus shown in the selected image, and sealing / adding a face to the cut edges.