Regarding a PhD advisor rejecting student due to health problems
In most cases, discrimination on the basis of disability or illness is wrong and in many places it is also illegal.  This applies in places where PhD students are considered employees and in places where they are not.
However, there are certain exceptions.  If the disability makes it impossible or unreasonably costly for the student to conduct their duties, discrimination might be permitted.  If the student has a health problem that makes the research unsafe, then discrimination might be mandatory.