Fellas I feel your pain. At least for the majority of you guys your equipment isn't in the worst environment imaginable. Basically everything I work on is around SALT. Yea....salt from your everyday Morton table salt, to solar salt they spread on your roads in the winter. Working on that equipment is no fun at all. But, here's a few little tricks I found out real quick to deal with broken bolts, studs, and rounded off heads.
1. If the bolt is big enough and not blind holes. Drill a decent size hole through the center of it. This acts as a relief for the melted bolt to run out of. Now remember, yes its a torch, but be very surgical and delicate with it. You can actually melt away at the bolt til you start seeing threads appear of whatever it is you are working on.
2. Blind holes are a little trickier to deal with. I've found that if you drill as near center as possible and steadily increase the bit one size at a time, you can keep going until you can use the same size tap and remove what material remains. Use TapMagic, Cutting Oil, or lube oil, I've found that regular engine oil works pretty good too.
3. If you know you are going to, or have a fear of "what if I break this off" try to make it easier on yourself. Lets say you're working on an exhaust manifold Cat 3300 series engines for example....take a cut off wheel, or burr grinder and pretty much take the nuts off if you fear breaking off the studs flush with the side of the head. What this lets you do is have something to grab onto with a stud remover, pliers, or you can cut the stud down long enough to weld fresh nuts onto whats left of the stud. Welding removal nuts to the studs will usually creat enough heat to help the studs out a little better.
4. Same thing with bolts....you tried an air gun...nothing, you tried a breaker bar....nothing. Heat the head up with the torch and still nothing? Cut the head off and try to save some something to grab onto. Usually the threads are corroded. PB blast and really any other oil lube travels towards heat. If you heat the stud or nut up, let it cool for a bit, then soak it with lube. THe lube will work its way into the threads slowly.
5. When worse comes to worse, and it pisses me off when I see this but it works. You're out of Helicoils or would take too long to get.....Say you drill out a 3/8" bolt and it takes the threads out too. Don't sweat it too much. If you've got metric Taps you can try to tap it out to 10mm, or the next Std. size up.