I actually published a paper on your last point many years ago. To me it's obvious that we need to use electric car batteries as storage for the grid. The infrastructure is already there. The software in the car should allow the user to specify their preference for how full to keep the battery at all times, and when they next plan to drive far, and the car can decide how it gets its battery charge to the required level in the available time. Adding in price incentives to use electricity when it's cheapest (when there's most supply vs demand) makes it even more attractive.