Does this fixture have on off switch?

The on/off function is controlled by an infrared sensor at one end of the primary unit but not the add-on extension unit. There's no pushbutton or toggle switch unless you add one, but if you interrupt the low voltage line between the wall unit and the primary lamp, you'll still have to wave your hand under the primary unit to turn it on or off.

Yes, the fixture has an on/off switch.