If you're asking what province is closer, the answer is Alberta. If you're asking what territory is closer, the answer is Yukon. Alaska borders British Columbia and the Yukon Territory.
Alaska
It is closer to travel from Alaska to Chicago, because the time distance is more. Yur Welcome!
Alaska.
California
Hawaii moves about 3 inches closer to Alaska each year
Alaska is closer to Washington.
Yes, Arizona is closer.
That would depend on what you call 'close'. Saskatchewan's southern border with the USA is at 49 degrees north latitude, so every point in Saskatchewan is closer to the north pole than it is to the equator.
Hawaii
Alaska
Alaska is much closer to Spain than to Argentina, especially if the most direct (trans-polar) distance is considered.