It’s hard to say what the most rare disease is, because we don’t know exactly how many people have each disease world wide. Most very rare diseases are genetic – they are caused by a rare mutation in the person’s genes. Therefore there is unlikely to be a full cure, but there might be ways to relieve the symptoms.
I don’t know. It could be that there are diseases so rare we don’t even know they exist. Sometimes it’s only when more than one person gets a disease that medical scientists can figure out that something is affecting people and making them sick. Doctors are like scientists, they share information of what they have found. Some diseases have been found because only small group of people all felt ill with the same symptoms . A famous case is called Legionnaires Disease, which was tracked down to a bacteria living in a dirty air vent!
Its hard to know what the most rare diseases are, because there are some diseases or illnesses that have only affected one or two people on the planet, but its very hard to study them in those situations. Usually this means that because we can’t study the disease we can’t produce a cure for it.