Can't help you with your initial question, since I've never check luggage through SIN

If you are going to stay at the Transit Hotel, make sure that you book the room well in advance. They tend to fill up pretty quick.

Also Terminal 1 is undergoing construction. They are doing it in the middle of the night so all you can hear is the jack hammer going until 3am... This was the case two weeks ago and I would assume that it will still be going on for some time. Bring some ear plugs or reserve a room in one of the other two terminals.