I only skimmed so forgive me if I'm off center here, but if the goal is to flash some lights when the beeper goes off then you don't need a processor at all. Use some analog parts, a high impedance input to a latching relay, maybe use an OpAmp. When the beeper goes off, sense the power to the beeper with the high impedance input and use that signal to latch the power on to a timer circuit that makes a light blink. Include a push button reset. You can put the lights right on top of each machine so it's obvious which one is in trouble. You might even be able to cobble this together with off the shelf parts from Amazon. If you want remote lights, just run some cat5 or something similar to trigger the remote lights.

He needs to identify which machine is in alarm using a single cable among the machines and to the remote location.

 

Very Simple Data Line ...
What if you used a single 16-Bit Shift Register Chip & a single Diode at each Station?
Station #1 pulls its Bit #0 low on Alarm
Station #2 pulls its Bit #1 low on Alarm
...
Station #10 pulls its Bit #9 low on Alarm

Unused Shift Register Inputs are tied High

The "Load Pulse" does two things ...
1) Captures the Alarm Status of each Machine into its local Shift Register and
2) Outputs the previous Serial Data as new Parallel Data at the Maintenance Office, in reverse order.

The "Clock" then pulses 16 times, to capture the Status from 16 Machines
The Output from each Machine is Or'd Low Active.

The Machines Clock-Out on the Rising Edge of the Clock Pulse
The Maintenance Office Clocks-In on the Falling Edge of the Clock Pulse

A slow 555 Timer Chip and a Counter Chip can produce ... 1 Load Pulse followed by 16 Clock Pulses, forever.

Could the 4 pair inside a Cat-5 Cable be used?
Pair 1 = Load Pulse + Gnd
Pair 2 = Clock + Gnd
Pair 3 = Data Line + Gnd
Pair 4 = Power + Gnd

 

Very Simple Data Line ...
What if you used a single 16-Bit Shift Register Chip & a single Diode at each Station?
View attachment 172752

Thanks for detailing what looks to be exactly the sort of thing I should be building. Unfortunately I have to sadly admit that shift registers are out of my comfort zone.
I will start some testing with the timed-duration relay thing for now as it is simple, a bit like me
If it does not work out as planned, I think I would next look to see how easy it is to run separate cables to each machine. That is going to be the easiest method of identification.