First off, isn't there another threaded hole in the hub for the disc retaining bolt?
Have you got the other bolt out of the caliper?
Remove the caliper and then remove the disc (you'll need to knock the disc off) and check, I thought there were two of these holes opposite each other on the hub, if so, just get a new retaining bolt and ignore the other.
If not, if there's enough hanging out, try a stud extractor, but I doubt there will be so get a good set of drill bits, drill out the broken bolt carefully, start with a smaller bit, say 5mm, then work up, try and get the first bit straight down the middle, with patience, you'll get it out.
This bolt hold the disc to the hub has four helpers, the four wheel bolts, so once the wheels back on, with or with out this little bolt, the disc's going nowhere.
As for the other broken bolt in the caliper, I'd hazzard a guess that it wasn't the right bolt in the first place, it usually has a fairly fine thread and that one in the pic looks wrong (I can not remember seeing a washer on any of these bolts either), if it was jammed without fully screwing in, the only thing that'll stop it half way down is the tread on the bolt and the caliper not matching.
If this is the case, this will be a problem, as it's already wreaked the thread in the caliper, the wrong threaded bolt will have started to cut a new thread in the caliper.
You could try drilling it yourself or take to an engineers, see if they can drill it out and put an thread insert in it, but as it's the brake I'd not want to chance anything and replace the caliper.