You can turn led's on and off as often as you want to above and below water. Halogens can be turned on and off but it's harder on the bulbs when you turn them on (just like any bulbed light) but it's only the HID's that shouldn't be turned back on immediately after turning them off.
Any dive light should be capable of being turned on or off underwater.
Any dive light should be capable of being turned on or off underwater.