Wiring three-axis accelerometer
Is COM the common ground for Vs and X,Y,Z outputs?


Yes, the evaluation board schematic shows the output filter capacitors from X, Y, and Z to COM.


  What is ST pin for? I couldn't figure out what it is used for?


Self test, check the datasheet, you probably don't need it.


  Should the power supply be constant? Can I use a battery? The reason I
  am asking these if I have 9V constant power supply and I use 3
  resistors to make a voltage divider, would it be ok?


No, use a proper regulator. See this question.


  How can I extend that 6-pin, 0.1 inch spaced header? Is there generic
  plug name?


That is about as generic a termination as you can get. Find yourself something through hole with .1" pitch on your favorite distributor's website. Look at Molex and Amphenol for a locking header and connector.