Only when the temp is low enough. they only run for a short time to warm the cylinder and assist with creating the required heat for combustion. You would be surprised how many glo-plugs don't work and the engine still does.

It is due to the variable resistance of the materials from non-running temps (air temp) to operating temp (my truck's exhaust temp is around 600 F driving around town and can exceed 1200 f under hard acceleration). Not many materials will stay within the required resistance range under that kind of temp change. To get the performance required would be cost prohibitive for road use vehicles. Yes, the can do it for race cars, because the costs involved are already very high.

Valves hitting the piston, not a huge problem...piston hits valve, big problem.