It will heat up on DC. It may or may not reach the temperature the AC voltage gave it, but it will provide heat.
It will work on smaller voltages, but smaller voltage = smaller heat. The way a heater works is it is basically one huge resistor. The only difference between it and a traditional resistor is that it's designed to dissipate the heat quickly (so you feel it instead). I would want to test it to be sure, but as far as I know, it will draw more current on 12v than it would on 120, but it will not pull an equivalent power. Sya it pulls 2A @ 120v, I do not think it will try to pull 20 A @ 12v. It will pull a higher amp draw, but it will just stop heating up at some point. You won't be happy with it at 12v, undervolting it that much will lead to very poor heating. If you wanted to run it at, say, 96v, or something close to 120, it will heat up close to what you would expect.
It will work on smaller voltages, but smaller voltage = smaller heat. The way a heater works is it is basically one huge resistor. The only difference between it and a traditional resistor is that it's designed to dissipate the heat quickly (so you feel it instead). I would want to test it to be sure, but as far as I know, it will draw more current on 12v than it would on 120, but it will not pull an equivalent power. Sya it pulls 2A @ 120v, I do not think it will try to pull 20 A @ 12v. It will pull a higher amp draw, but it will just stop heating up at some point. You won't be happy with it at 12v, undervolting it that much will lead to very poor heating. If you wanted to run it at, say, 96v, or something close to 120, it will heat up close to what you would expect.