When I take of this jumper ( at the above screenshot that is on my motor shield ) I can put 1 power supply to power shield and 1 power supply to my arduino at the same time without any problem, right ? thanks.
Yes, that is the jumper I thought you were talking about. Take that off and you can power the motors with their own supply.
The grounds will be connected together through the motor shield, as long as you connect both leads to the Ext_Pwr pins.
As for the current, the two outer ICs are the motor driver chips; read the numbers and Google for the datasheets. I think that might be the same motor shield that I have, it has two L293D chips on it. They are rated at 600mA max, 1.2A peak.
However, without a heatsink, they may get quite hot at 600mA.