Nope, Major hasn't been killing anyone. From the episodes, he has only taken care of 3 people so far. Remember how he kept taking off names from the list? He's still checking people out, but probably lying about some of them so that he doesn't have to kidnap everyone (last episode those 8 people he took off the list…

She's investigating these disappearances but also the disappearances of the rich people Blaine got rid of (like the astronaut). Hopefully the full blame is put on Blaine and Max Rager.