Are study visas only given for the set time of the course?

I think you may need to apply for an F type. When applying for this type, you need to provide the embassy with an invitation letter from the school and the letter states how long you will stay in China. The consular officer will give you a stay duration based on this letter. However, it's possible that the duration can be longer if you fill in the application fom with an earlier expected arrival date and give brief information about your itinerary.