I grew up very close to Hockenheim and went a couple of times, but don't recall in detail where to park.
Free parking ist mostly on a "field", i.e. maybe not the best for a new car
Connecting in Mannheim is no issue, there normally is a shuttle from Hockenheim main station to the circuit. And: during rush hour public transport will be way faster than crawling through the traffic-jam (which can be found all around the Motodrom).
Hope you have some spots in the area on the sightseeing list besides Hockenheimring !?