Hello there,
The headlights on my fiat grande are always on,can they be turned off or it's a safety feature from the manufacturer.There's no provision on the MENU ESC button to turn them off like some other fiat models.

When you say your head lights. Do you mean dipped beam ?
If so, the control stalk on my GP where your lights are wipers are fails and sticks the lights on. The module would have to be replaced.
If not, and it's just side lights could be daytime running lights but that should be within the menus

did you find the issue? my punto is the same the dipped beam always on , switch does nothing x

I have just had this fault on my car. I removed the twin stalk assy and stripped it down. Found the 5hin red wire was broken. Soldered together again and it’s all ok now, was a bit tricky baring the wires and ‘tinning’ them prior to soldering together.

See my reply to the one previous to this.