Is this possible? Dynamically changing fieldsets on node creation
You probably could apply some woodoo to save the data :) But : you would have hard times retreiving it. Node displays only the defined fields, Views only show the fields and so on.

I would suggest not using webform, but simply defining those quizes as new node types and save them, together witha reference to a record about the answer (if it is important).

It might be handy to use eck instead and create an entity type and bundles for each quiz - so you dont have to deal with all the settings on node, just the fields.