only other one I can add is the cutting torch. if the tap is broken off in aluminum you can blow it out with the ol fire ax. aluminum transfers heat way better than steel so if you heat the steel really quick you can burn it out of the hole with not too much damage to the aluminum, though you will probably need a helicoil. and yes, I have actually done this.
best thing is to not need this kind of anguish in the first place. tap with a good lube, turn in a half, maybe 3/4 of a turn, and then out a quarter, keep the chips cleaned out of the flutes.
as for broken studs... first is a left handed drill, if that doesn't work I try to drill it down the center "on size" , if I screw that up I helicoil it. I really don't even bother with easy outs anymore. a broken ez can be drilled with a cobalt though