So no ground or neutral is needed to the element itself?
Nope.
Ground is there on appliances as a safety in case the wiring somehow has an issue and puts electricity to the case. Gives the electricity a very easy path to use instead of going through the human body. Not having a ground won't affect operation of an appliance, only how badly you get hurt if something in it fails (of course, the smarter the appliance, the more likely it is that it will know that it isn't grounded and not work at all.
Neutral is only for 120V, typically if a 240V appliance uses the neutral it's because something in the control electronics is made to use 120V. The way 120/240 works is the neutral is in the exact middle of the 240V windings, so that's why when running a lot of 120V items on a generator you try to balance how they are plugged in/wired so that you aren't overloading one half of the windings.
240V is more efficient, it uses the same size wire for the amount of amperage used as a 120V item, so for the same price for all the wires you can use literally twice the amount of power.
