It is not true that they do not have overnight rooms, there are a few rooms (maybe 7?) But they are only available from 1700 to 0900. You can book them online.

入館料が日本円で1500円、深夜料金が日本円で1500円。合計3000円で個室ではないリラックスルームの利用となります。 個室の客室利用は日本円で5000～となります。 館外へ出るときは、一度精算をしないとだめだったと思います。 空港内のエアターミナルホテルに宿泊の場合は、この温泉施設が入館料無料で利用出来ます。エアターミナルホテルは出入り自由だと思います。

They do but it’s not a locker. They place it inside a storage room. That’s why they will ask you to get all of the stuff that you need because once they place it in the storage area, you cannot request to get some of the stuff you have forgotten in the luggage. They are very strict about it. Yes, they speak passable english and they can understand what you need. You will be given a medium sized locker to store ur stuff (ones you are able to carry) in the women or men’s bathroom onsen area.

Hello! Nope no need just wait for them to open at around 8am if I remember correctly. You can just walk in directly without reservation. Thats what I did