ESD Mat circuit theory
Question 1: The internal components are all eventually connected to
  the conductive metal, so won't they absorb the static discharge from
  your body?


A wrist strap ensures that the potential between you and the computer is near 0V instead of thousands of volts that comes from clothing and walking across the floor. The damage comes from current flowing from you into the small gates that make up transistors. If the voltage between you and another object is 0V no current can flow.


  Question 2: Wouldn't this just create an open circuit to ground?


No, when you connect the wrist strap to the mat, they really mean to ground, look at the diagram below and wrist strap two. Wrist straps should be bought with the 1MΩ resistor built in.




  Answer to Questions 4-10:


An ideal ESD setup will lower all potentials to near 0V (which means connecting it to earth ground). There will be no current transfer into parts because there is no voltage to start with, it has been lowered to ground by a wrist strap or mat. These have a 1MΩ resistor to prevent a short circuit to ground in the event the user or other voltage should come in contact with the mat or wrist strap. 

If you have a wrist strap only to the computer that's probably fine in most cases. A better setup is one with a mat and a wrist strap to ground. A true ESD controlled environment has the floor, the table surface (and no paper, or plastics that are not ESD safe), tools and lab coats (to prevent electric fields from clothing) and the humidity of the air controlled.