Can you trace range through the galactic core (turn track)?
No, the center sector turn tracker is out of play for all purposes.
If two people tie for first place, does second place still exist? For instance, if two people tie on a region for first and each get three points, does the person with the next most power get three points or one point (only for presence)?
Yes, the second place player still gets their points for second place, so it it essentially a three way tie for score. It creates a nice incentive for 1st place players to not tie!