When traveling abroad through a school program, What type of medical information do universities require be reported?

generally, any communicable diseases and all accidents

Check both specific requirements of the university AND general requirements of the country's gov't for student visa.

It should say on the form as if the information is required or optional.  Through a school program, ask your school. Get facts direct form the source. 

My daughter did a study aboard program form the US to the UK and disclosed she has asthma. It was for her own safety. 

I don't understand the question. Universities usually require you to have insurance. But most of the countries you might go to have universal coverage. I know people who had medical problems when on study abroad programs. THey got treated for practically nothing- one had her appendix out, one had a broken leg, one had a rare tumor removed. I don't think any of this was reported to the university- medical information is usually private. 

generally, any communicable diseases and all accidents

whatever you think they need to know