Hi
To try and clear thing up a bit the system can be broken down into 3
sections.
1 Speech.
This is a 3 wire system using a speech module located in the front panel and
a handset shaped like a phone containing an earpiece and a microphone.
It works like the old intercom units rather than a phone.
Wiring is simple .
12v AC to the model 61 speech amp terminals C + and H -
The earpiece and mic' then connect to R mic' T earpiece and O common for
both.
All phones are in parallel.

2 Signalling.
The early handsets had an AC buzzer inside (just a coil with a metal plate
above it) but your picture is of the newer 801 series which has an
electronic warbler cct on the pcb of the phone.
This works just like a door bell.
12 ac from C+ on speech amp to common on all push buttons at front panel.
Other side of push button to I terminal on handset.
Circuit completes in handset by internal connection to O terminal on pcb at
phone.

3 Lock release.
AC lock connects to C terminal of speech amp and is activated by handset via
Z terminal on phone.
This connects to O at handset when release button is pressed on handset.

The handset wiring is simple the earpiece section has the earphone/mic
inserts sharing a common return wire .
These then feed via the coiled flex to the base unit where they are either
soldered directly to the pcb or plug in on 3 micro bullet type pins.

From experience I find that the handsets are very reliable and the fault is
normal the speech amp as it is open (via the front grill) to the weather and
insects.

As to repairing the handsets I normally just replace them as they are only
around £10 -£15 and as they say time is money.
But if you like tinkering or are stuck for parts then repairs are simple 2
screws hold the earpiece together and wiring is exposed all terminals are
fixed with Mini spade clips so you can easily swap out parts.

Working on these regularly I have loads of 'bits' in my junk box so if you
are really stuck let me know.

HTH
CJ