Actually, as far as I can see, the nearest Supercharger is in Goleta. There are other chargers around town including some fast chargers and Tesla Destination Chargers at several hotels. Check Plugshare for details.
There are other superchargers in Santa Barbara, though.
No
No, they do not have an available supercharger unless your car is being serviced, or possibly an extreme emergency, I know, it makes no sense at all.
Its best to look at your contract ...
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