Theres a reverse set type of bits that are good to use & sometimes just the drilling process, will back what is left of the bolt out.
Once you get the broken bolt out, just remember real good all you had to go through to get it out & put some anti-seize on the new bolt or stud. Not every bolt or stud needs locktite, cause long as the threads in the hole & those on the bolt or stud are clean it will hold.
Neil