After seeing your photos, I'm now pretty sure that your motor is actually a Smart Pie:
You can see that your motor is slightly different to my front and rear Smart Pies, but both of mine have internal controllers and therefore do not have the hollow axle:
I did not realised that the external Smart Pie was so different to the internal ones, as the picture on the GM website does not show the wire exiting the axle.
The Smart Pie on the right is a lot smaller and less powerful than the Magic Pie II shown on the left:
As the Smart Pie is not so powerful, it will probably need some pedal assistance to help it up steeper hills.
Although, your 20" wheel should produce 35% more forward thrust propelling the bike than my 700c
(27") Smart Pie.
The Smart Pie and the BAC-0283P controller should both run fine on 24V, 36V or 48V, as long as the controller is not drawing more than ~18 Amps maximum.
Above 18 Amps, the motor begins to run less efficiently and will generate a lot more heat under sustained heavy load.
Alan