You can still join school while in H1 by showing h1 papers.As far as I know changing status from H1 to f1 is not easy . you have to file change of status to USCIS which takes 4-6 months. They will verify if you have been maintaining your h1 status properly or not. If you get rejected you'll get a notice to leave the country within 30 days. more info on www.murthy.com