HC-05 HardwareSerial 1, 2, 3 vs SoftwareSerial library

The first thing to think about is why would you ever want to use software serial on a Mega.

Then, in the highly unlikely event that you must to it, use the pins recommended, not the hardware serial pins.

Because there are many tutorial doing that way... even on Mega. And when you're beginner, you begin following tutorials, and first tuto I followed were doing that.

Next thing to think about is the purpose of the state pin and why you need to use it. It simply provides an alternative to the State LED on the board and you might suppose that the only time to use it is when you can't see the one already provided. This could happen, but if you are the first person to ever use STATE it wouldn't surprise me.

It's exactly what I need, to replace the module onboard small red LED because this one should be hidden in the global device.
If found example using the STATE pin :

I've read somewhere else that to be carefull do not make error with wire and make digitalWrite(pin, HIGH) from arduino pin to HC-05 STATE pin.

If you have actually damaged something, it is most probably due to user abuse.

My module and arduino have less than one mounth... and I work on it around 1h a day...

You can probably test the situation by disconnecting the state pin and trying to use the HC-05 in the normal manner.

Yes, I'm going to retry that next time...