My 06 Mustang has a wierd car alarm.?
Well I had a focus and it did the same thing to me. The first one the car thinks you are stealing it so I sets off an alarm to alert people to look at it. The second thing yes the alarm will go off if you use the key to unlock after using the key fob to unlock it. I don't know why but this is something that ford does. If you lock it using either the button on the door panel or the key then the alarm will not go off next time you use the key when unlocking. Ford didn't think ahead and put a receiver in the door lock for the transponder to turn the alarm off.
go to the passenger side lock door with remote then unlock the door with the key that should your problem