In reverse order - In an old-shape punto you definetly can't leave the lights on without the keys in the ignition.
If your wheel stops spinning and you've got it out of gear it does sound like a wheel bearing. If it doesn't go away when you have the engine on or off, and doesn't go away wether the clutch is in or out then it's either a problem with the wheel bearing or the transmission.
Just because you've got it in neutral or clutched in doesn't mean bits of the transmission still aren't turning. Everything from the wheel hubs, the driveshafts, the final drive, and the output shaft and gears are all spinning as long as you're moving, so it could be any one of those.
See if the sound changes when you corner - if it does it points to a bearing or driveshaft issue. If it doesn't, it could well be your transmission. Grinding tends to be bearing-related, whereas whurring is a gear thing (unless you're in a rally car like I was last week, in which case it means you haven't done the wheel bolts up).
Hope that's some help.