It goes even further if i'm not mistaken, you have to prove you have TWO parking spaces, one at home and one at work.
I didn't know, but it would be logical, yes.
The fun part is, there is no strong definition of how much space you need to park a car, you have to prove you can actually park your car in the space you declare. An officer follows you to your parking place, and stands there watching your maneuvers.
I don't think you have to prove that. In big cities like Tokyo and Osaka, most people use public transport to commute anyway. Although it's not mandatory, in practice every company will reimburse your commuting costs if you take public transportation.
Yes. And in Tokyo transportation is cheap. Taxis only cost 710 yen per kilometer and all trains stop 12h30 at night.
BTW Paris is testing the casual car rental strategy also.