Yes, no.
Yes!
I'd add though that any variac designed to buck or boost the incoming AC line has the best load regulation at the 'DOT' where it neither bucks or boosts. A 240V variac on 120V input will have reduced flux in the core, and although I'm not sure about this, I'd bet the regulation, or waveform distortion would be degraded using the 240V variac on half voltage.
Jack, what do you need? I have some small to mid size dudes here in a pile...
Jim
Wd5JKO