An interesting question. 

My hypothesis is that there is an infinitely countable set of possible questions humans can think of. 

A question is a at least one or more ordered set of words.

Words are created by humans.

Words can be created as we abstract a set of concepts or objects.

The set of possible combinations of words therefore increases naturally.

It is therefore permissible to claim that humans are able to formulate an infinitely countable number of questions.