Is there a place in the new terminal where you can store your luggage until your arrival time? Or, are you able to check your luggage in the morning and then return for your arrival slot?

Yes you can. There will be person there to take your luggage if you not going to carry it your self.

I am not 100% sure butt I think you can leave it at the port with their staff: so far I was able to do the check in right away when they opened it so I never needed to leave the luggage.