1) The fact that you have applied for student visa and that the visa application has been denied will remain on file in the VIS system, and it can be used by competent authorities whenever there is an authorization to access your file. They do not have a specific list of people who have been denied their application, but the information will remain in the system associated with your file. See REGULATION (EC) No 810/2009 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 13 July 2009, establishing a Community Code on Visas (Visa Code), Article 32. title Refusal of a visa:
5. Information on a refused visa shall be entered into the VIS
in accordance with Article 12 of the VIS Regulation.
2) The denial shall be furnished in writing, and it shall state the reason for not giving you the visa. See REGULATION (EC) No 810/2009 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 13 July 2009, establishing a Community Code on Visas (Visa Code), Article 32. title Refusal of a visa:
3. Applicants who have been refused a visa shall have the
right to appeal. Appeals shall be conducted against the Member
State that has taken the final decision on the application and in
accordance with the national law of that Member State. Member
States shall provide applicants with information regarding the
procedure to be followed in the event of an appeal, as specified
in Annex VI.
and Article 47, title Information to the general public:
(h) that negative decisions on applications must be notified to
the applicant, that such decisions must state the reasons on
which they are based and that applicants whose applications
are refused have a right to appeal, with information
regarding the procedure to be followed in the event of an
appeal, including the competent authority, as well as the
time limit for lodging an appeal;
Can you post the reason?
3) The time limit is 30 days (Tribunal Superior de Justicia de Madrid).
4) The fact that you have applied for study visa does not deprive you of your "visa-free" status as a tourist. As a Canadian you are allowed to travel to Spain without the need to obtain visa as long as you satisfy the 90/180 rule. The student-visa refusal does not change this.
Good luck to you.