All numbers we have are not supporting those claims.

Since the summer months see the highest traffic on the Autobahn due to school holidays and vacation, this might actually be a clever solution to store surplus "green energy" into car batteries instead of letting it go to waste ;)

1. Currently it's about 50/50 for renewable vs fossil fuels. However the trend is that renewables are growing and fossil fuel usage (mostly coal) is declining. You can see some cool graphs on the Wikipedia page for energy in Germany

2. No