I am a non-EU student and I was in the same situation before starting my PhD. My supervisor requested the university to waive-off the remaining portion of the fees and apply EU rate fees (as the scholarship covers only home/EU rate fees). His request was honored and now I have to pay EU rate fees for all the years. So in my opinion, discussing the problem with supervisor can help.

You will need atleast TOEFL or IELTS score to prove your English language proficiency, as your native language is not English.