Can a Death Note Owner be killed with their own Death Note? Can the owner of Death Note be killed if another random person knows their face and name, writes the owners name in the owner's own Death Note? with a sheet torn out from it?
There is no rule currently known which prevents any person from killing the owner of a death note under normal circumstances.  

The only reasons a death note will not work on a person assuming that the victims name and face are known are: 


  
  the victim is very young
  the victim is very old (124 years old or older)
  the victim is already about to die in the next few seconds
  someone already misspelled the victims name too many times
  the victim's name was written in a second death note simultaneously (victim still will die)
  the victim's name was already written in any death note in a valid way (time of death before end of natural life span).
  


(Please edit if I missed any.)

I almost always have to note on these questions that the rules available to us about the Death Note are not complete. In fact, the rules themselves state that even the shinigami do not know all of the rules about how a death note works.