I'm very confused. It sounds like OP and GF arrived on day one with two others who were scheduled to arrive the next day.

If that means that all four shared one room (with a rate for two people) the first night, then the hotel was justified in being concerned that two extra people were trying to stay for free, possibly violating fire codes, etc. This could have resulted in the spying behavior, not sending all luggage to room, and certain comments.

OTOH, if all four just used the first room to shower and change while waiting for the second room to be ready that day, then the hotel might have been confused about this.

BTW, it's not unusual for overseas hotels to insist that guests check out at the desk and sign a bill before leaving.