My impression is, if the goverment were to lower the taxes, you would see car dealers and gas stations raise their prices. The market is supporting what people are willing to pay with or without goverment interference. But I'm no expert so hey I might be wrong.
An X amount tax will raise the price of the commodity by some amount less than X
yes. the reason is that when prices go up people buy less, prompting the highest-price sellers (those who are least eager to sell) to simply not sell. Lower the price of car-use in Denmark and more people will use cars, but not to such an extent that the total (after-tax) amount people spend on cars will stay the same.