Washington
The US State of North Carolina is farther north than South Carolina.
Alaska is the furthest North US state, AND has the highest mountains in the US.
Maine
Alaska
The state that is closest to the north pole is simply the furthest north state which is Alaska.
Delaware.
The State of Maine is the northernmost US state on the Atlantic coast.
Montana is the state that has the northernmost monument to the Confederacy.
Virginia
Estonia. Estonia is nothernmost Baltic state while Latvia is the middle one.
If, by "country", you refer to the sovereign territory of a Nation-State, and if by "furthest North" you mean extends furthest to the North, then the answer is almost certainly Denmark, which includes the territory of Greenland. Canada (Ellesmere Island) would run a close second, followed by Russia (Franz Josef Land) and Norway (Svalbard). It is possible that there are minor islands further to the North than Greenland, which might be part of the territory of another Nation-State (most probably Canada, Russia, Norway, Finland, or Sweden), but that seems unlikely.
The furthest state from the state of Michigan would be the state of Hawaii and the state of Alaska would come in the second place.