Anyone knows how to open the boot if "indipendent lock of boot" is turned on and you got the car running?

(Without changing the config and close and reopen the central locking or turning off the car and take off the key indeed)

Try pressing the central locking button, although i thing that's what's meant to be. If you have the indipendent boot lock on you must turn off the engine, get off the car and place the key into the lock to open it.
Hope i helped!

Andreas (CY)
Fiat Stilo 1.6 3Door Dynamic, Metallic Black, 16" Alloys, Dual Zone Climate Control, Steering Wheel Radio Buttons.