Automotive chassis is positively charged compared to earth, is this a problem?
Aswer to a:

The car is not earthed trough the tires. Remember that sometimes someone get a static shock when leaving a car.

Answer to b:

Some people purchase and install a special flexible wire (carbon strap) that lays on the ground removing static charge. You can most probably find it in a car shop.

Answer to c:

Since the current drops to zero everything seems to be ok. So dont worry.