Once I got the cylinder head out, I tried heating the stud with a propane torch then pounding it out with a mallet, but the stubborn stud didn't want to come out. After trying for almost an hour, I decided to give up and bring the cylinder head to Mini Mania and ask Brian the mechanic to remove it for me, which he did with some effort.
Engine Block - Cylinders, and New Head Gasket
I removed the carbon deposit off the cylinder head with a wire brush attached to a drill. I was more careful with the pistons - since the pistons are dished, I was able to leave a puddle of carb cleaner on the cylinder, carefully soaked it away with a shop towel, then scrubbed it off with my fingers. For the carbon deposits away from the piston dish, I had to hand-crank each piston to the top, then carefully remove them with a razor blade out-to-in, to push the deposits into the dish.
