In a 3 player game, do all of the position tracks get shifted to the 1-3 spots, and if so, does this mean that House Stark starts with the Sword?

Yes, all houses shift positions to fill only the first three positions. The houses that are now on position 1 get their respective Tokens (Throne, sword, Raven).

In the Raven track, you should modify the number of stars each player gets:

First (the holder of the Raven token) gets 3 stars

Second gets 2 stars

Third gets 1 star.

Awesome, thanks. We assumed that they would all shift, but I did not realize the Raven track adjustment - that would be a significant change!