Four-wheel drive is definitely required if you go off the road at all. Also, check your rental insurance as some damage is not covered especially to the undercarriage of the car.

The glacier itself is heavily crevassed and I would not try to climb on it without proper equipment. There's a plaque at the base of the path memorializing 2 German hikers who went on the glacier some years ago - and never came back. That said, you can walk quite some distance up the path (which runs alongside the glacier). There may be some rock scrambling, depending on how far up you go. The road from the main highway to the parking area is quite bumpy and full of holes; you must drive slowly but you do not need 4WD to do it.