As far as I know you can stay at their restaurant or lobby coffee shop. But if you want a room then you need to check-in.
Well, I stayed for a short while in daytime once.
Better call them and check...
Not at all, I think as the hotel is of good reputation. Even if they permit, you will have to pay for 1 night.
Not sure whether this is the kind of hotel you are looking for.
Get an answer from The Peninsula Chittagong staff and past guests.