On your 1st question, most if not all EV’s have 2 batteries, the main traction battery and a standard 12v one. The traction battery is recharged either by plugging in or regenerative braking and powers the motor and A/C only. The 12v one though is charged like it is is an ICE via an alternator. This battery usually covers all the traditional tasks of a car battery, with the exception of the Air conditioning.
The second question, I would guess that the extra weight and cost of such a system, just isn’t practical for the amount of power it could provide. The most logical (to me) system would be fitting cars with solar roofs, I believe the Hyundai Ioniq5 has this as an option, but for some reason not a UK one.
Previous Motability Cars
2006 - 2009 Skoda Superb VR6 2.0tdi
2009 - 2012 Citroen C5 2.0tdi VTR Nav
2012 - 2015 Nissan Qashqai 1.5dci tekna
2015 - 2018 Ford Kuga 2.0tdi Titanium X
2018 - 2021 BMW 220d X drive 2 Series Active Luxury
2021 - 2023 Hyundai Kona Electric Premium SE
2023 - Hyundai Kona Electric Ultimate