Washington
Alaska is the furthest North US state, AND has the highest mountains in the US.
The US State of North Carolina is farther north than South Carolina.
The State of Maine is the northernmost US state on the Atlantic coast.
Alaska
Maine
The state that is closest to the north pole is simply the furthest north state which is Alaska.
Delaware.
Montana is the state that has the northernmost monument to the Confederacy.
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.
Virginia
Estonia. Estonia is nothernmost Baltic state while Latvia is the middle one.
Belize if the farthest country north.