Is it problem to feed the Arduino with high current batteries?

I have 2 batteries (12V 7Ah). How should I feed the Arduino(DUE)?

Use one of the batteries, and the barrel jack.

There are limits to how much power you can draw from the Due 5V and 3.3V outputs (no motors or servos), and if you try to draw too much the on board regulators will overheat and shut down.

jremington:
if you try to draw too much

The keyword there is "draw". You could use a 12V car battery which is capable of providing some 100s of Amps, but it won't foist those on you.