Please let me know how to file a COS from H4 to F1

Please let me know how to file a COS from H4 to F1 ? do i get i 20 form only after applying to a university or college. can i get i20 before applying to any university.

Last date to apply to a university for Fall 2013 is 1st may. can i apply upto 1 st may or i should do it well in advance

You get I-20 only after the school approves your admission. You can talk to the university about their deadlines and the earliest date they accept the application. Then taking a margn of 2-3 months you can file the COS.