There are multiple reasons. The most important reason is not having belief within themselves, that somehow they are not meant to heal and that this serves as a punishment. This punishment factor is wrapped up with negative emotions that attack the body. Another reason is there is no belief in anything that is not seen, felt or heard. For most, in order for there to be a belief it has to be something tangible. It cannot be an unknown. This lack of belief impedes any healing that can be done. And some have chosen to not heal because their illness defines them and their existence.
2) Are there cases where a disease is divine in nature and not meant to be cured but rather serves a, greater purpose? If so, how will I recognize such cases?
This requires a complex answer. There are layers of existence within one existence. Multiple existences side by side that have no connection to the other. Within one existence a person can be ill yet, in another existence the person is not ill. It really is an interrelated energy field that bypasses and overlaps one another. There are four energy fields that make up the layers of existence which is all part of one existence. Somehow, a person became ill during the bypass or overlapping phase through another layer of existence. Within one layer of existence the person is ill but within the other three layers of existence they are not ill. It is a part of the energy path of existence. The only way to recognize a case like this is to ask. If a person has been identified in this case, help can be requested.
3) Are there ways in which someone can better prepare themselves to receive the healing so it is more effective? If so, what are they?
Be open to receive. Have faith in the process. And be open to the word.
4) Am I meant to focus primarily on healing of the physical body or the emotions and mental realms as well? Does healing always occur on all levels simultaneously?
You are meant to work on helping all living beings to help each obtain total truth. Which means to heal every aspect of the being. Healing does not occur simultaneously on all levels. First it is the emotional healing and then leads to the remaining levels of healing.