I don't understand how a car maker can represent a whole nation ? Why is it that Toyota is strongly associated with the image of Japanese businesses but other giants, like Panasonic are not ?

If there is one sector that is really in trouble in Japan right now it's not the car makers but the airlines. JAL and ANA are both on the verge of bankruptcy. This would leave Japan without any national airline. I suppose that the competitions from the other (usually very good) Asian airlines, like Korean Air, Cathay Pacific, Thai Airways, Malaysian Airlines or Singapore Airlines have a lot to do with it. European airlines seem more competitive too. I or my wife have been dozens of times between Japan and Europe and we never used JAL or ANA, almost always European airlines (because they are cheaper and just as good). Toyota is a long way from being bankrupt.