Need help reverse engineering and understanding a small circuit
D2 is a half wave rectifier that creates DC from the transformer to provide power to the CPU.  C1 and C3 are in parallel and smooth the DC with the unknown component probably being a zener diode or shunt regulator to control the supply voltage to the circuitry.

Although it looks unusual being in the negative rail D2 is probably arranged like that so that the voltages are convenient for sensing and driving the transformer with Q1 for back communication.

C3 resonates the transformer to the frequency of the carrier used for transferring power and communications. I would expect a frequency in the 100-200kHz range.

The AC signal passes through D1 to pin PE1 on the CPU for the communication. The combination of D1 and R1 limit the voltage that the CPU sees to acceptable values.

Q1 is used for the CPU to send data back to the base unit. When it is told to conduct by the MCU putting PE1 high it drives the voltage from C1 across the secondary of the transformer - the base unit will be able to pick that up.

I suspect it implements a half duplex sequence where the base unit transmits some data by varying duty cycle of the signal into the transformer which at the same time will put energy into C2 to power the front panel.

The transmitter will then stop sending and wait for the front panel to send information back to the base unit. The sequence will then repeat. The sequence has to be be performed fairly quickly (10s or 100s of times per second) as the front panel is operating entirely from the energy in C1 during the time it is sending information back to the base unit.

Since AREF is connected to ground it implies the ADC is not being used - it is normally recommended to leave it open though.