what if one digital pin is HIGH and connects the GND?

I don't want to have this obviously, but in case, when a digital pin is at HIGH status, and it is shorted (connects the GND) without any resistor.

Will it simply been pulled down and the mcu still be safe? Or it will have a very high chance (almost sure) to break itself?

I would like to consider this worst case scenario just make the design and the circuit robust and functional in all the conditions.

I assume you're talking about an output pin? You'll get excess current, the chip may overheat and you might damage the chip.

The "absolute maximum" allowable current from an output pin is 40mA. At 5V, that works-out to a minimum output resistance of 125 Ohms. (A direct short to ground or Vcc is zero Ohms.)

I had an output-short to ground once. The program still ran (the other I/0 pins were still working, etc.). I didn't touch the chip so I don't know if it was hot. It took me several minutes to troubleshoot but the chip survived with no obvious damage.

okay. what if accidentally applying voltage to those output pin from external battery?

For the ATmega Arduinos the output drivers on the chip have about 30 to 40 ohms of on-resistance, so that you get currents of perhaps 150mA (much larger than the absolute maximum for the pin and even for the whole chip perhaps).

Don't expect the chip to survive undamaged, that pin may become damaged as its output transistor cooks. You
may be lucky and still have it function, but its a good idea to check the pin carefully if you do this, make sure it still drives in both directions, hasn't developed leakage current when supposed to be off/input.

If very unlucky such a short might trigger CMOS latchup of the chip. Then it will suddenly get very hot and pull
high currents until power cycled. This is not good!