There are actually two separate things that people might consider as "black boxes.' There's the Event Data Recorder (EDR) that serves as a traditional blackbox where in the event of a crash it'll record various data like 5 seconds before the crash; things like gas pedal, brake pedal positions, accelerometer data of the car, speed ,steering angle, etc. The EDR records data at a very high frequency, probably something like 200-1000Hz. Too much data to send it all back to the Mothership. As far as I know, after a crash you need an
EDR Kit and physical access to the car to retrieve this kind of data. Here's an
example of a report when you send in your EDR data to tesla to generate one. Because Tesla needs you to submit the EDR data for you to generate the report, I think this implies that the data in the EDR is not sent to the Tesla Mothership. By regulation there's an EDR on every car since ~2006.
There's all kinds of other data that your car does send to the mothership, things like location data, charge data, basically anything on Teslafi or Teslamate are data that your car sends to the mothership. This stuff probably gets recorded and sent to the mothership around 1 - 0.1Hz; something far more managable OTA. As far as I know you can't access the data history from Tesla. On my Teslamate I only have data going back to when I started logging it. I'd be surprised however if the full data history isn't store somewhere on Tesla servers. I mean Tesla pulled logs t
o disprove a negative NYT review story way back in 2013 and Elon seems pretty confident that Autopilot wasn't on in that recent crash in TX. Ultimately I think for this part of the question, only someone inside Tesla HQ would know.
Edit: changed the link for the NYT story to the tesla blog version of the events. There's some example of what data they were able to retrieve from there.