The response from your Uni has clearly illustrated their application and assessment procedures. On the requirments of your school, you have to send your application documents to the International Student Office. In my opinon, you can email your eletronic docuemts ( including scanned papers and files) to the department you want to apply to and then you are supposed to receive some recommendations from the school. If your supervisor is available and your qualification is approved, you will be required to send your certificate documents. Many Universities are of pleasure to allocate supervisors to the potential applicants, based on applicants' majors and background. So, it is unnecessary to contact with your prospective professor in advance if you feel unconvinient.
By the way, according to what you wrote above, it seems that you had a great chance to succeed in your application for Ph.d. Considering the bad situation, you can also be offered a place of Master Degree by Research. In that case, it is easy for you to transfer it to Ph.d degree in the cousrse fo your master cadidature.
So, get out there and do it!