Filing COS from h4 to f1

I am currently on h4,planning to apply for COS from h4 to f1.I got admit from a university and going to start my college from this fall 2015.
My doubt is
1.Do we have to apply COS on our own? [OR]
2.Do the university that I got admit from will apply for COS? [OR]
3.Do we have to seek for any employer to file for COS?
And one more thing is
My DSO is saying that they can provide me an i20 for SPRING 2016.As I am going to start the classes in Fall 2015,can I apply for COS with spring semester i20 in the month of August 2015?
Please help me out.