I am attending a one week conference/summer school at a University, I would also like to spend an extra week touring Copenhagen. An official from the University said I cannot tick Study since participants of the summer school are not affiliated with the university. Should I tick both 'Business' and 'Tourism'?
If you can tick multiple boxes, tick both Business and Tourism. If you cannot, tick Business. Do not tick the 'Study' box.
'Study' is for official courses through an accredited education body. Ticking that box will cause trouble for yourself, as they will assume you need a student visa (which you don't). 'Study' has a specific definition which your summer school does not fall into.