The 18-8 or 304 stainless steels are "bare minmum" 18% chromium. Soft stuff and thus crappy for fasteners. 316 stainless steel is a superior material for corrosion resistance but still below what a medium carbon equivalent will do. The 400 series stainless steels offer hardenability for things like knife blades. You can see the equivalent problem if you look in a deck screw catalog like the old McFeelys which had torque-to-fail data for various wood screws.
Stainless machine-threaded fasteners also have the infuriating quality of galling like crazy on stainless steel nuts. Since essentially no oxide coating is present there is a lot of micro-welding going on in an all-stainless steel external and internal thread, eventually bigger "snowballs" jam up the threadform. Anti-seize is the best policy in my book. Or go to titanium fasteners if your wallet is fat enough
As far as how to remove a twisted-off fastener, I'd just leave it alone. Excavation of the surrounding area is the only sure way, depending on the depth some miniature carbide burrs (think dental tool) could work but have limited depth. Plus the excavated hole is highly unlikely to be suitable for another fastener, so one must move over to a new location anyway.
