1) The battery is always balancing itself. But.. the calibration of the range meter may be off after 30k miles. You can get it to recalibrate by draining the battery down close to zero.
2) Supercharging is more damaging to the battery than even high-amperage home charging. It takes a lot of Supercharging to hurt the battery, but if that's the only way you're charging it would be a problem for the battery pack's health. If you can charge at home, that's recommended for battery health, your own convenience, and not taking up a Supercharger stall that somebody driving a long distance could use. Outside of California that last point isn't a big problem, but as Teslas become more common it will be.
3) Not mentioned in your post, but constantly charging to 100% will also damage the battery. Tesla recommends 90% for day-to-day driving, though I set my S at 60-70% when I know I'm not going to need all that range.