My 4 y/o is the same way... not about killing ect... but acting identical in the other ways. It's actually typical of this age. They are testing boundaries please don't resort to medicine

Consistency is key and lots of times the teachers at head start seem to push for kids to be medicated to make life easier on them. Google gifted children and you will find that all of these traits are actually of extremely intelligent children... Something worth looking into.