Broken bolt

Only bolts in an exhaut manifold are the choke wells. All others are nuts on studs. Take Rob's advice and drown them. If they dont loosen with a steady pull, try and tighten a bit to break bond. If there is nothing left to grab, you can drill it out and pick out the shell but you need to center punch it first so the bit wont follow the angled or convex break plane. If you got lefty drill bits, those are the best as they have a chance to unscrew while cutting them. Sometimes when the head snaps off, there is no longer tension on the broken part and it will unscrew rather easily once something can turn it, Even a thin welding rod tacked ti it. The end studs on Mopar V8 heads are famous for busting as the holes are not blind to coolant.