I would like to know the function of an AUX terminal which is between the motor ports.
It’s a generic half-bridge power output, i.e. it can be driven to VBUS or 0V or neither.
I think the developers didn’t know what they wanted to do with it when they first designed it. You could use it as a high power audio amplifier for a loudspeaker. 
However, in the current firmware, its function is to dump power via the brake resistor when necessary, to prevent the VBUS voltage rising above 56V or whatever limit has been configured.
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Hi, could I use the AUX +/- to power an Arduino Mega via a Buck-converter? My 56v battery can accept re-gen fro the motors.
No, but you can just hang an Arduino Mega off the 5V rail instead (~ 1A limit)
Thanks that would simplify the circuit. The only reason I wanted 9v supply to the Arduino, is that other self-balancing robot projects have had problems with voltage-dip ‘brown outs’ under high-torque demand situations, causing re-sets of the balance calibration (it falls over).