You can prove immunity if you have a positive Hepatitis B blood Anti-Body test (HbsAB). For MMR you can do an Immunity Titers test, and if it comes back positive we can use this as proof of immunity.
Yes, when you pick up your reports you will be given a sealed envelope that contains the original copy and you will also receive a scanned copy for your own records.
No fasting is required for these tests
The medical exam is valid for two years after the date of examine (DOE), the form itself should be submitted along with I-485 within 60 days of the doctors signature date which can be located on page six. Please consult your lawyer further on this.