I entered new contact information for my student and then it wasn't there when I went back

Information on the Student Profile saves automatically as you enter it.   There is nothing you need to do to make it “stick”.  Some users mistakenly think the "Refresh" button is a way to save their information.  Actually, the opposite is true.  The "Refresh" button reloads the original information.  The only time you would click refresh is if the program wasn't responding and didn't bring the information onto the screen.  This would be extremely rare.  If your student contact data is changing or disappearing, it is getting updated by the SIS.  You will need to go to your district's SIS and update the new contact information there. 
 

I changed the student from EL to RFEP and it asked for a date.  Where do I get that?

If the student has been reclassified from EL to RFEP (Reclassified Fully English Proficient) then there will be a written record of that decision with a date on it.  If the documentation is not in the student's cumulative file, contact the Language Acquisition Office to get a copy of the Reclassification Form.
 

Our district health records for vision and hearing only have month and year for the results, but SIRAS wants a specific day.

Just go ahead and enter a day in the middle of the month for the first time you are entering the data for your students this first year.  In subsequent years, make note of the date the nurse checks the students in your program.  Ask for a list of all your students immediately after the vision and/or hearing testing and enter all the information for your caseload on the Medical tab of the Student Profile (Under Student Info) so whenever you are ready to do an IEP, the vision and hearing results will automatically be entered onto the Present Levels page.

On the Next Year's Data tab, I can't seem to enter the name of the school.

You must enter the name of the District for next year before you get access to the list of schools in the district.  Enter SELPA before District before School.