You can buy (almost?) any part directly from Tesla as a plain Joe [1], but you may need a VIN for certain parts (mainly the actual computers?).
In the event you want to DIY a repair, Tesla publishes all their service manuals they use at their service centers (e.g. [2]) and you can can even use the exact same software their technicians use for the deeper repairs, albeit at a price that is expensive if you're a plain Joe, but for a repair shop it doesn't seem to be terribly expensive.
On the topic of 3rd party parts, there isn't quite as robust a marketplace.
That's actually a lot less than I was expecting. Toyota's is $1500/year.