There is a 12V battery but that is only used for the 12V systems (radio, dash, headlights, wipers, etc.). The car has a lot of common parts with the ICE Focus. The drive battery (or high-voltage-battery) is more like 350V.
To charge the car with solar in a reasonable amount of time would require a lot more square area than is on the car (like the roof). There are people who charge their FFEs with a solar plant on their house.
The supercharger system is proprietary to Tesla and even though Tesla has said anyone can use their patents no automaker has yet to do so.
Ford has signed on with the SAE CCS fast charging method but has yet to produce a car utilizing it. This year at CES they did briefly show a prototype FFE with CCS.
