The AI = no accidents: I can see it on rails and zero chance in the next 20y to have any AI that can drive in winter conditions, or even fog.
There is no way to build any 'minimal' frame for $1k with any material that's remotely lightweight. Heck, even the current battery technology is sort of low energy density. You get around 220Wh per kg (or 0.8MJ vs gasoline's 46MJ). A hundred kg would be 22kWh. With a lightweight body - 400kg (~900lbs) [price not withstanding], highly aerodynamic model on good asphalt - I'd say 250km (155miles in freedom units) is realistic - but then you need cooling system to charge them, unless you consider they can be hot-swapped (or willing to wait longer).
What you suggest is proper futuristic stuff taken from a sci-fi flick, none of it would happen anytime soon.
