Balks

When a pitcher throws to an unoccupied base, it is (usually) a balk...

8a. With a runner on 2nd and the right-handed pitcher on the rubber in the set position, the runner at 2nd breaks for 3rd. The pitcher makes a legal step toward 3rd, throws to 3rd base and easily retires the runner at 3rd as he steals. The offensive coach wants a balk because the pitcher threw to an unoccupied base. What is the call?

Call
It is a balk for the pitcher to throw (or fake a throw) to an unoccupied base and in this situation 3rd base was unoccupied as the pitcher assumed his pitching position.
 
However, 6.2.4b indicates that a pitcher can throw to a base in order to put out a runner or drive back a runner.

Bonus Question: Is the call different if the runner that is stealing 3rd runs about one-third of the way to 3rd while the pitcher throws to 3rd, but the runner retreats safety back to 2nd? When the pitcher threw to 3rd, did he balk?

Call
So, in both situations, in HF rules, this is not a balk.

In MLB, the runner must be stealing (not faking a steal) in order not to balk.