enquiry on visa to beijing (urgent)

I am an undergraduate student from national university of Singapore holding a singapore passport. I am traveling from singapore to beijing for 3 months internship with a university there on 15th May but will only be back in singapore on 12th May.
1. May I know which type to apply for?
2. Do I have to apply personally or can my parent apply on my behalf?
3. Is it possible to obtain it before my morning flight on 15th May and how much will it cost, thank you!