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, use the pins recommended, not the hardware serial pins.
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.
I've tried with Serial2 and Serial3... It was working one time on Serial3 and after no more. I don't understand... I don't know if I damage something and if the problem comes from the arduino HardwareSerial port or from my HC-05 module
If you have actually damaged something, it is most probably due to user abuse. I don't think it is easy to do any damage to Mega by using the state pin as the bluetooth module has a current limiting resistor parallel to that for the on-board LED. You can probably test the situation by disconnecting the state pin and trying to use the HC-05 in the normal manner.