1 and 2) Yes, 0 is 0 and sometimes may be less than 0. (As you saw) If you haven't discharged the pack below 10% in a while and haven't charged to 100% in a while, the car may not know how much energy is left. It doesn't know where the bottom of the battery is. Also worth noting, once you're below about 8% SOC, you lose a significant amount of energy in the battery and inverter as heat due to higher impedance in the cells and higher current required to get the same power out of the inverter, and this can't be measured as it doesn't pass through the current shunt in the battery that the car uses to determine how much energy has been pulled out of the battery and put back in.
Other 2) Navigation can be off by a bit, but usually if you're continuing to do the same thing it'll continue to predict the same thing. If it starts to predict you'll arrive at less than 4% SOC, you will like arrive at 2% SOC due to the heat losses mentioned above if you're still on the highway at 6%. In those cases, SLOW THE CRAP DOWN. If it's predicting you'll arrive at 7%, though, you'll likely arrive at 7% unless you drive like a demon and constantly pass people.
3) A 50 mile cushion may be excessive between superchargers (lower rate of charge on arrival) but a 25-30 mile buffer (based on PROJECTED RANGE over the last 30 miles) is definitely worth having if it's cold, may rain, or a few other factors. (Speeding being the big one)
4) As you learned, tow mode is basically neutral. Neutral is basically just disengaging the parking brake and energizing the drive line, and neutral achieves the same thing without actually energizing the driveline.
5) You may get one mile, you may get 10 feet, you may get 6 miles. This all depends on the true current SOC.
6) I've been using my Model S for road trips for work, and i've put 6000 miles on it in the last 3 weeks. More often than not, I can leave a supercharger 10 minutes before it says I can, and then I get to my next one between 9% and 4% SOC, depending on how fast I drive. If I do 70MPH it's closer to 9% and 80MPH will get me there at 4% SOC. When things start looking scary, I'll just bump the cruise down 5MPH and wait for the prediction to update. More often than not, slowing down 5MPH from 80MPH will save about 2% over a 140 mile trip, and then 70MPH will get another 3%. This is also on hot days with the AC running at 70F and no rain. During the winter, with rain, I'll use a much much larger buffer (20%) and go slower. My average supercharger stop, at a correctly functioning supercharger (that's another story...) is about 15-20 minutes. This means a normally 7.5 hour trip is about a 9 hour trip, so the overhead for charging is very small, and the stops make the drives much less tiring. (Even without AP) When I explain this to some of my "Go, go, go!" friends they nearly die at the idea of "losing" 90 minutes, but they're also the kind to fill up, dive 500 miles at once, not drink anything, not eat, and not stop to pee. For NORMAL people, though, the Model S is a fantastic road trip car and makes driving a true pleasure that's not tiring at all. (And if it does get tiring, a 45 minute supercharger nap will usually make it better.)
