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To my limited knowledge most (maybe all) of the software in Tesla model S can be updated over the air, using cars cellular internet connection.

That's correct. It's possible for a service center to load software over a wire, but that's only necessary when something goes wrong. In the normal course of events, the car pops up a little alert saying there's a software update available, and asking when you want to install it. Updates are free forever (although one expects that updates for older hardware will stop being made eventually). It's basically like an iPhone in this regard.

That's not uniformly true. Mini dealers would upgrade firmware for cars out of warranty.

Yep, ownership doesn't matter.