i deal with rusted and sheared off bolts all the time on cars living in the rust belt.
EZ outs are terrible. i don't even own them because once you do a lot of work like this you realize that if something actually comes out with them - that same thing would come out with other methods that are far less risky. and they cause enormous grief when they shear off, which happens a lot.
personally i say throw them away - but if you're forced to use one NEVER give it any blunt force or impact. they are hard but brittle - think sort of like concrete blocks - it can withstand enormous weight but drop it 8 inches and it'll crack. that's what ez outs are like.
if rust appears to be an issue use a high grade penetrant (WD40 is not a penetrant) like liquid wrench, PB blaster or if you're lucky enough to have a supply of YIELD that is industrial strength penetrant. soak it for as many days as you can...even if you have to spray and get to work that's fine too.
heat the exterior around the threads with a torch...even a dinky propane torch will help. the expanding/contracting of the metal can help break it loose. it will also help penetrant to seap.
the best way to use heat while removing is to heat the metal surrounding the bolt without heating the bolt itself, then try to extract the bolt immediately - expanding the surrounding metal helps. once the heat dissipates to the bolt it's all the same and not helping.
left handed drill bits are your friend. best bet is to start with a very small one to create a guide hole then use a larger one. worst case you drill the bolt out until there's nothing left but a thin shell in which case it will come out.
or you could just drill the entire thing out and use a thread repair kit. they're very easy to use.
if there's any metal left to work with, welding a nut onto the remaining stud is the way to go.
the ghetto fix if it's not a very structural component is to drill a smaller hole within the bolt hole, then tap it and just use a smaller bolt to attach whatever was attached there before. i've used this method for reattaching things like brackets, etc, mostly benign stuff. have to use judgement call here based on useage, loads, how big the bolt is, etc. being a steering gear arm - if it's a single point of failure you probably don't want to but i can't see the sizes and stuff you have to work with.