1. If you are already in US, you can do a Change of Status to F1, talk to your DSO at new school. If you are not in US, then you will need to get new F1 visa stamped.
2. Well, you need to check on this with DSO and CBP officer to confirm this. Sometimes, if the same SEVIS ID exists, you may not need to...but, again, I am not sure, you need to confirm with CBP officer by emailing them or talk to DSO.
3. You need to check with your DSO, who issued your I20.