What stops a university form doing anything it wants is the contract you entered with the university when you enrolled. (I'm writing from the perspective of a student, not faculty). You and they are bound by the contract, and part of that contract will be a clear outline of academic processes such as ethics, grading, class requirements and test taking, as well as penalties for cheating and plagiarism. That contract will be outlined in your student handbook.
That handbook and contract will also clearly outline (or should) the grievance process and remediation for both students and faculty. Since you feel that the university is not being fair, you need to start with investigating that formal grievance process and look into gathering your materials and filing a complaint. The college will have an office that handles such grievances; you need to find it and talk to them.
If they are a private college, yes, they do have their "own rules," but some aspects of federal, provincial and local civil and criminal law will still apply. Be aware that the school contract may bind you to arbitration - which means you have to deal with the college on all matters - and you may not be able to go to a public court on a civil matter.
A lawyer will be able to tell if you are bound by arbitration and if so, that's the end of the road. If not, a lawyer will tell you if you have a criminal or civil case. In any event, the grievance process at the U will more than likely be your first step.
If by chance criminal misconduct is found during the grievance process, then a federal, provincial or local prosecutor would be involved; we would assume the university would be forthcoming if that need appeared.