It depends on the conditions like what size it is, is it accessible and how it broke, like was it over tightened or cross threaded. If it was cross threaded you will probably have to drill it out and install a heli-coil to repair the damaged threads. If it was over tightened and snapped off there are several ways to go about it. One would be to carefully drill down the center of the broken stud and use an easy-out tool. Another would be to weld a nut onto what is left of the broken stud, allow to cool and turn it out. There are also counterclockwise drill bits out there that can drill in and catch the stud to back it out.
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Are you handy with a center punch, and a drill? If so, the best way to do this is to drill a hole in the center of the stud, and along with penetrating oil, an/or heat from a torch, use an easyout to extract the broken stud from the intake.
You may have to get a nut splitter, a grinder, or a hammer and chisel to get nut off and then have stud replaced. Hopefully the splines in the drum haven't been torn out and a new stud can be pressed in. If not, you might be running a lug nut short (which is not at all wise) or you'll have to come up with a new drum. Auto recyclers live for challenges like this.
Depends on which pulley but most have several bolts holding them on. You can remove the broken bolt or simply not worry about it.
This is a really tough problem. The tie rod end is a ball and socket arrangement with a tapered stud. The tapered stud usually is a force fit into the steering knuckle. What you've done is loosen that force fit and now the whole stud is turning. First, I have to ask if you removed the cotter key from the castle nut before you tried removing it? If not, then that's why the stud is turning. If the cotter key is out, then try using a C clamp to squeeze the stud back into the steering knuckle so you can get some resistance. Also, you can try using a die to rethread the rusted threads on the stud. If all else fails, you'll have to get a nut cracker and split the castle nut. Then you'll have to buy a new nut. Rick
get a tap and die set and follow the instructions.