I'm confused by your question/post. 

Are you saying you want to play a witch, with mind reading abilities? -- Then the answer is no.

Are you saying you want to play a witch who's specialization is 'Quaestum'.  -- Then yes

You can play any age character you want. 

Gringore Academy is a College place, but the RP also revolves around the humans and supernaturals of the town not just the school, so any age is fine. teenagers can also take college classes if they want. Gringore is a school for supernaturals only, so the degrees/credits/certification are only usable in the supernatural culture/world.