Older fire alarm control panels (the Simplex 4005 control panel counts as an older panel) sometimes had a "City Circuit" output. The City Circuit was used as a direct means of calling the fire department over dedicated telephone lines. Nowadays, this type of communication is not used, but the card is still there.
To find out more about your City Circuit card, Google the words "Simplex 4005 city circuit", and close to the top will be information about the City Circuit card, and the Simplex 4005.
On the circuit card itself, check the disconnect switches, one of them might be in the wrong position.
Also, there may be something wrong with the card, or another switch somewhere else is set wrong, or a plug has come loose in the panel, but basically, the card might not be working right. To fix the problem, you may have to get the fire alarm system serviced.
When the system is being serviced, if the card isn't being used at all, you might even want to have the card removed. (Don't remove the card yourself because then you can't get rid of the trouble on the panel.)
The other thing you mention is the tone that's driving everyone crazy. To communicate alarms and troubles to the monitoring company, it sounds like you have an external box doing the dialing. If so, that box might be making the annoying tone. This is a red box fairly close by, or at least in earshot of the fire alarm panel.
Take my word for it, no one can tell where this tone is coming from. To confirm that you've found it, find the red box and put your ear next to it. Once you've found the box, on the right hand side of it, there may be a small button. Press the button for about 3 seconds and the box will go silent.
That annoying tone is a trouble reminder sound, though. Just to remind you that there's a trouble on the system, every 24 hours this box will turn on the tone again. To silence the red communicator box permanently, you will have to fix the trouble with the Simplex 4005.
Keep in mind also, the call center doesn't receive a continuous trouble signal. They only receive a one-time signal that says there's trouble. Until all troubles are fixed, they won't receive any other trouble signal.
They are receiving their daily test of the phone lines, so they can tell you that part of the fire alarm system is working. However, beyond receiving the one-time turning on or off of the alarm, supervisory, and trouble signals, they can't tell if there's anything wrong with your system. That probably explains why they don't think there's a problem.