I thought Alaska was a USA state.
If you sail from Vancouver you go through US immigration when boarding the ship and from then on you are in US territory. If you are sailing from Seward then you are already in the USA and you are in it until reaching Vancouver. Re tours, I don't know if it's the same now (it is some years since I went there) but beware that if you go on the White Pass railroad trip in Skagway the return bus trip may well go via Canada and you have to go through US immigration on the way back. Don't forget your passport otherwise you could be in big trouble!
USA Dollars but be careful if you make your own arrangements and have problems your on your own,if you book through the ship and you get problems your going to get help,but you will save by making your own arrangements.
We did our own thing its cheaper, but beware that the weather can sometimes spoil the best laid plans,Alaska is dollars but the will accept canadian dollars.Have a great trip it will stay with you for eve.