Is it using rectified 14V for the drive circuitry, with the mosfets acting as a gate for rectified 230V? Can a voltage regulator actually step 230 down to 14?
Yes. Rectified mains voltage at around 300V is used for the motor and 14V for the drive circuitry controlling all mosfets.
There is a 8pin ic on both sided of the mosfets. Those are probably half bridge mosfet drivers, each controlling two mosfets for one motor phase.
It is impossible to see on the pictures how the regulator is connected to the mains input.
Often a capacitive dropper circuit is used for generating a low voltage supply from mains. But in this case this probably doesn't work because of the bridge rectifier.
There are some special voltage regulators capable from generating a low voltage from mains voltage (either a high voltage linear regulator or a phase control circuit using only part of the mains cycle). But it could also be a mosfet acting as a linear voltage regulator (there is a diode next to the regulator, it could be a zener diode).
Trying to read the markings on that part is the easiest way. Otherwise you need to reverse engineer the circuit. Look at the connections between mains, the regulator and the 14V rail to get an idea how the voltage regulator works.
Working on such circuits is difficult and dangerous, because everything is connected to mains. I recommend using an isolation transformer when working on the circuit.
I would start with verfifying all voltages (+320V on the large capacitor, +14V on the small one next to the regulator.
If both voltage are ok, then I would probably replace the small electrolytic capacitors.