What determines the maximum discharge rate of a battery and how can I create a high current power supply from batteries?
12A with 0.4ohm series resistance would use up all the battery voltage leaving nothing for the motors. 12A * 0.4 = 4.8V.

To determine the maximum current you can take out of the batteries you first need to know what minimum voltage you need for the load.

For example if the minimum voltage you need to drive the servos is 4V that allows 0.8V drop across the internal resistance.

0.8V across 0.4 ohm is 2Amps.

Yes, you can put strings in parallel to increase the current.  From the previous calculation each string would give 2A. To get 10A you would need 5 strings in parallel.

You can't some extra headroom by adding an additional series cell.

For example if you had 5 series cells in each string you could take 5A before the voltage dropped from the 6V @ no-load to the 4V minimum voltage.

With this in mind you could get 10A peak with just 2 strings of 5 cells or 10 cells total.  The lifetime would be less as the capacity would only be for two batteries in parallel.

Be aware that the voltage of the cells is not constant.  When fresh the cells are probably about 1.5V then drops as the batteries are used.  Cells are normally reckoned to have no usable energy when they have dropped to about 0.9V.