The car of course has onboard storage and processing capabilities... Data would be stored in the exact same place it would if they were learning from the whole fleet. Moreover, it's possible Tesla outsources processing of the data to their servers. It's honestly pure speculation at this point.
Furthermore, I was under the impression that v6.2 didn't have lane keeping / full autopilot?
It has multiple levels of onboard processing and storage. The question is what does what?
Speculation is the car stores the data to be uploaded for fleet learning on an SD card. I'm not sure where else it would store this data.
The Nvidia Tegra 3 is used for the Digital Cockpit, but it doesn't serve any AP function aside from UI/UX.
The Lane-Keeping/Auto-pilot is done via a Mobile Eye chip, but Mobile Eyes software runs there. I tend to see the MobileEye processor as something you load pre-trained DNN's in. A DNN being a trained Deep Neural network. Where the training of it took place offline (at Tesla or MobileEye). The DNN handles things like detecting lanes, cars (visually), speed limit signs, etc). It doesn't do any self-learning. I imagine most of the DNN's used for various functions (Object Detection, Lane Detection) is provided by MobileEye as libraries. Where Tesla can pick and choose what they want. Like the Tesla can do Speed Limit sign detection, but not Stop-Light detection.
The biggest hole I've seen in this communities understanding of Tesla's Autopilot system is how the system learns.
For learning to happen it has to have a feedback loop. Something that tells it what the "correct" way was.
If I take an exit one day, but then I don't take an exit the next day it's going to be awfully confused.
If I have to deviate because of construction (onto the shoulder) it's going to be confused.
Fleet learning is massively important because it brings so much data to the table. Not only does it bring the data to the table, but it allows humans to decide which is the "correct" way.
The only really informative technical article on the Tesla AutoPilot I've seen so far is this, but it doesn't go into the fleet learning that much.
Exclusive: The Tesla AutoPilot - An In-Depth Look At The Technology Behind the Engineering Marvel
As to the other question -
V6.2 had TACC and Blind Spot Monitoring (limited side spot monitoring).
V7.0 brought Lane-Keeping, and Side Spot Monitoring.
Technically the Side Spot Monitoring is not in the AP package, but I consider it to be within the realm of the Driver assist system.