There is the general consensus that 85% of operating vehicles will die and 50% will restart and operate normally. There is a video on YouTube that shows a test car being hit. It dies and won't even turn over but the battery is still good and it's power windows continue to operate. Pre 1972 vehicles are considered EMP proof because they don't have electronics installed.

Yes, a power cord will take in an EMP but it, like the antenna must be at least 10". Most power cords are approx 3-5 FEET in length.

Any Farraday cage must be well grounded in order to work.

Edited to include additional info.