Well... mA-hours doesn't tell you how much maximum current you can draw. It's a measure of how long the battery will last. [u]Here[/u] is a datasheet I found for a AA battery. It says:
2,850 mAh (to 0.8 volts)
(Rated capacity at 25 mA continuous drain)
So in this case, 2850mAh means they measured it at 25mA, and it took 114 hours for the voltage to drop to 0.8V.
On this particular datasheet, I didn't see a maximum current rating, but the discharge graphs show dischage current up to 1000mA, so I assume that's "safe".
For my circuit, I have added 4 similar rating aa batteries in series. My question is, what is the maximum current that can be drawn from this setup?
The total current rating should be the same, but the voltage is summed. With 4 batteries the total energy available (milliwatt hours) will be 4 times that of one battery.
My geared motors work at 32 mA and their stall current is around 500 mA @ 6v. If I limit the current to 32 mA, and if the load in the motor increases, will it slow the motor down?
Right! With limited current, the motor will slow-down (or stall) with a lighter mechanical load than the motor can otherwise handle (at around 500mA). "Conservation of energy"... If you want more mechanical power out, you need to put more electrical power in. 
Also, if the motor draws 32mA with no-load (or with a given light-load), it probably won't start with 32mA. You generally need a "kick" of current to overcome the initial friction and inertia.
Also, What is the max current drawn, if I add battries with 2100 mAh and 1600 mAh together.
In series? Probably unpredictible results... The 1600 mAh will most likely die first, and then you'll mostly be getting whatever voltage remains from the higher capacity battery.
If you've got a flashlight that takes two batteries, and you put-in one carbon-zinc and one alkaline, nothing bad will happen, except the carbon-zinc battery will die first and the light will go very dim with only the alkaline supplying power.