Yes, you are required to pay import tax on the car when you bring it into the country. In the end you break about even. You could of course bring it in and avoid import, but it's high risk, sooner or later you get busted for driving and owning a car with swedish license plates as a Norwegian. (A foreigner can keep his car here for about 1 year before getting Norwegian license plates.)

No. But one would be required to pay customs duties (import tax, really) — so then one is paying the same amount as just buying it in the country.