There is no reason for most tourists to use a car in cities, other for day trips out of town. Parking overnight is usually multi-storey garage nearby, with attendants.

Yes there is usually free parking outside the cities. But there is also paid parking outside cities.

Highway Toll system works like most other countries.

http://global.c-nexco.co.jp/en/toll/methods.html

Payment by ETC may be available at car rental companies in Hokkaido and a few odd places elsewhere.