According to your hotel’s website, you definitely want to go to Kutchan station since they have a free shuttle from Kutchan to your hotel. There is a Minami Otaru station but looks like it’s over one hour away from Kutchan station.

Yes, Otaru station has storage lockers.

Hi there. You will be on the right level - the train you want will be on the adjoining platform. If you already have your ticket through to New Chitose it is right there for you. If you need to get a ticket you will need to go down on the escalator - you will not get list as it is a small station. The rapid airport train runs every half hour from Otaru, and it takes an hour and a quarter to reach the airport, which us the terminus, so you cannot go wrong. Each station is announced as it us approached and English is used as well as Japanese. (Do not catch the stopping train as it rakes much longer - the overhead signs on the station platform are very clear.) A carriage in the centre of the train - possibly carriage 4 - is for reserved seats only - if I recall properly, this is clearly marked. It us clearly marked on the edge of the platform where the carriage doors will be. It is a very easy, efficient trip.