Broken exhaust manifold bolts

If the studs are sticking out from the manifold surface you can heat the head and see if a quality Vice Grip type plier will take them out. If they are below the surface, welding a nut onto them can extract them. If they are buried (like I see in one of your photos, You need to drill them out. Carefully start with a small bit 1/8" and keep drilling bigger. You can try a easy out (I prefer straight splined types with the proper sized drill bit) Remember, if you break off a drill bit or a easy out you are pretty much screwed. I have used carbide tipped masonry bits with limited success.