I really want to make plastic jewellery and brooches like this one
Don't call the Fire Department. It's not their responsibility. If the detectors are indeed wired to your alarm system then call the Alarm Company. But I rather doubt that they are. Re-read the instructions and double check all connections. Try swapping the one in the hallway for one in another location. If the problem remains with the detector, it is bad. If the problem remains with the location, you may have a loose connection in that box.
anywhere from home depot to lowes A.K.A. your local home improvement store^ as stated above,
when you replace the bateries they need to be put in a certain order the manual should explain that