[mehrdadn]

Can you say "Quoi est-ce?" and avoid that ambiguity (and correspondingly, "Qui est-ce?")? Or would that be wrong?

[jobigoud]

"Qui est-ce ?" is correct. "Quoi est-ce ?" is not. "Quand est-ce" and "Où est-ce" work. "Comment est-ce ?" doesn't really work by itself but could work with something after it, like "Comment est ce film ?".

All of these work and sound more natural in spoken language if you flip and say C'est quoi ? C'est qui ? C'est quand ? etc.

[bdauvergne]

You can't, the "liaison" is mandatory between "quoi" and "est".