What is the max current for the LEGO EV3 motors (pin 1-2)? The LEGO EV3 Hardware developer kit says that the first and second pin of output port provides a current of max of 700 mA with 1 A  but the motors appendixes don't have the maximum current that can I (safely) supply to the motor.
What is the max current that the motors can safely drain?
The amperage drawn by any motor depends on the voltage supplied and the resistance (load) on the axle. Even if you provide the motor with more ampers than it could safely take, it will only consume as much as the voltage and load require.
As for the maximum value that each motor can draw when supplied with 9V, potentially unlimited amperage and given an unlimited load to move (stalled), see the comprehensive component characteristics comparison compilation by Philo. Here we can see that when given 9V, the EV3 large and medium motors will consume 1.8 A and 780 mA respectively when stalled, so those are the maximum values they can draw from any 9V power supply.
See also this Q&amp;A over at Electronics.SE about motors, the relevant values and their relations.