The first answer is, with more AH behind your output, will lower your full circuit resistance. Expect slightly better system efficiency, much better battery efficiency, thus a much longer battery life, and a tad more top speed against the wind and up hills on max programmed controller settings, because the paralleled batteries will slump less volts under heavier loads.
The power through the controller is limited via a shunt that controls the controllers pulses time width "PWM" (Pulse Width Modulation) at each phase switching, so the differences between batteries are only cosmetic from the controller stage unless you change the programming or shunt resistance values.
The answer to question 2 is, yes and no.
The motor is dumb. It can absorb 1000's of watts at any given moment of time, what makes the Smart Pie so smart is the controller I believe. So if you change nothing in the controller, do not raise the battery voltage, or rewind the motor, then the answer is No! More AH will not make the motor more powerful with a small controller set to factory settings.
Its a controller thing that is limiting the motor.
Now the better question is, if you manage to get more than 400 watts into your Smart Pie, how "LONG" will the motor tolerate the load? You can run these motors much higher than their rating depending on what you use them for.
The larger motors I reckon for most people, its safe up to 2 kilowatts at 48v, too much current, can flex the coils and they wear out, plus at the lower voltages, the impedance of the motor may cause heat pushing massive wads of amps through the copper parallel winding strands. The Pie is not wound with lots of conductor strands, so lower volts at stupid high currents with a big load will see more heat than with higher volts at lower current.
The MP runs most efficient with most controllers between 36v and 72v between 25 to 50 amps.
These medium sized MP3's will run fine at common voltages at 50 amps for most people, but not so much with the controllers.
The smaller mini motors, I wouldn't go over 18 amps and 36v.
And for the HBS series 30 amps at 48v is plenty.
It depends on your average riding, for example hills, wind, and rider weight.
I carry some heavy loads often. I found a well tuned Pie can pull a lot of weight limited perfectly and the motor will not get hot. Maybe a little more slowly, but the MP hubs definitely have the diesel motor power thing going on for their weight class.
If you want more speed, you need to increase the voltage. This will give you both more torque and speed. As to why voltage can give torque on our motors, but more amps dosent give more speed "research induction, wind resistance, ion engines and dev your own theory.
1v @ 1 miliamp can get you moving at the speed of light if you have enough time and almost zero resistance, but not down here on earth.
Mass Speed, Torque, and Resistance has a linked relationship with Voltage, Current and electrical Resistance in motors.
For instance, it is commonly said that more current offer more torque, however, to drive a motor faster one requires more torque.
It is the way we view torque when we parallel our packs or series the mix up occurs. Torque too is a physical attribute of mass, through the electromagnetic conversion process, can be paralleled, or series as current is an integral and essential component of any higher voltage induction that does occurs when stacking voltage cells up to higher potentials. When you add a series pack you still get that packs amp hour in watts, and that amp hour torque thus must be is translated into the speed, as you get to your destination faster, you save amp hours.
Our controllers performance can exploit a lot of the interactions between amps/torque/voltage/speed, and pull of some neat tricks, and our batteries can make us go nice and fast, but it work up to a point where the worst enemy of all hits us, and this is the big hills and wind resistances.
Batteries simply do not yet have the tech or energy density to do this big hill climb or impossible break neck speeds very well. If we could make a battery 3 times lighter, then we will be competing with some good source.
