1) You will never connect your batterys directly to the motor. You will have an ESC (electronic speed controller) regulating the power going to the motor. If the ESC is supplying 10A to the motor, the battery will be happy with it. I don't know about your motor so I can't say whats the max power it can handle.

2)I don't know what bms is. If thats same as ESC (regulates the amount of power going to the motor), maybe 20A.

3) Yes, your pack will also have discharge rate of 3c. What determines the power of your motor is watts (W), not amps or volts individually. Power=Voltage*Current so if you have 2 packs in series, you can get double the power compared to a single pack.