KittyKatz, will attempt to hit the target in this attempt within the borders of your rules. The purpose of the universe is not to be morally or physically perfect, but to provide a place where spiritual beings can choose to love or reject God, to live with Him forever in a new, perfect universe, or reject Him and live apart from Him for eternity. It would not be possible to make this choice in a universe in which all moral choices are restricted to only good choices. One can not choose between good and bad if bad did not exist. It is very logical, if all evil was eliminated, we are bound to partial free will by where our choices have a predestined outcome. If humans could only make good choices, is this really free will, or just the creation of robots, like computers.
Do you think the atheist who loves his wife, who would never be unfaithful in falling to the temptation of sleeping with her closest friend, if the situation presented itself, would stand down from his absolute free will within the confines of his personal ability to have the choice. With a decison and full responsibility of choice, by not falling to temptation, is not the atheists love for his wife greater by not committing a evil act against her that she may never discover occured. The latter is analogous to changing the laws of the universe to restrict the exercise of evil. There is no way to eliminate all evil through changing the laws of physics, since it originates within the human mind. So, the only way to eliminate all evil is to actually restrict the functioning of the human mind, in other words, restrict free will. So, all claims that God could prevent all evil choices, but allow free will are specious. Though, it seems God designed the laws of the universe so that human beings are unable to exhibit unlimited amounts of evil, or we would have destroyed ourself by this point in time. The tuning is optimal for the restriction of most temporary, bounded evil, while still allowing free will. If you want to create eternal-perfect designs, you must understand thermodynamics in where one of the laws would need to be removed, which would make the universe completely different. There would be no stars, no electromagnetic radiation (including light), and no way to design machines (including biological ones) that depend on heat/energy flow. This means that creatures would not be powered by food or metabolic processes. Creatures designed for such a universe could never die a natural death, since death is dependent upon the operation of the second law. However, the description of this hypothetical universe corresponds almost exactly to the bible's description of heaven.
The problem about heaven is that there is no ability to choose good versus evil, since there is no evil. This lack of choice is the reason that God instituted a two creation design, the first in which free will beings could make choices, and the second to reward those beings who choose to be with God in His second creation. In the sum of all things, Adam was commanded not to eat of the tree of the knowledge of good and evil, in the middle of the garden. Sometime after Adam was placed in the garden, Eve was created and the scene was set for Adam and Eve to obey or reject God. God had to give Adam and Eve a choice. Without free will to choose, Adam and Eve would have been mere puppets. Did the fruit have magical powers, or was it just the fact that they went against the orders of the commander in chief because satan used the oldest ploy in his playbook of deceit, God is a cosmic killjoy who is trying to keep something good from you. The presence of evil is due to the spiritual component of our nature, something that animals do not possess. A false assumption is that love allows the object of that love to do whatever he or she wants. However, this permissive kind of "love" isn't really love at all. A parent or not, you will recognize that allowing children to do whatever they want to do is not loving at all, right.
As for the application of prayer, its not the adoration, confession, thanksgiving but the supplication you are directing your question towards. In making specific requests on Gods to-do list, its pray for other first, then yourself. The scenario where a Christian (Jehovah's Witness) decides that prayer is the way that their child should be healed, so he forsakes medical treatment and the child dies, is just blind faith parenting. Miracles are rare and have a specific purpose, any claim for one on the basis of faith is no reason to call off inquiry, declaring it a miracle.
You asked if God heals the sick, though you really have to be giving legitimacy to medicine as a healing art. Prayer is not a soliloquy, it is a dialogue between man and God and is objective as well as subjective. We should be able to agree that intercessory prayer provides no scientific evidence either confirming or negating the healing effectiveness. Though self request prayer would not be so inconclusive, for it is therapeutically in its association with a positive mind set. Obviously this would work for SJD, though not yourself.
The healings of Jesus were given as a sign of the legitimacy of His claim of Messiahship, since the O.T said that the Messiah would heal the blind and the deaf. God didn't create diseases, though, He did create a system they could come to be, though, thats an entire thread alone. Could open your eyes to medicine and make you question why the corporate industry are driven to providing treatment, not cures. We put ourselves in many medical positions, and God shouldn't be a saftey net. To quote Rostos; "God is not some personal genie".
With your Island scenario, wouldn't God have clearly revealed Himself in nature and in the hearts of people. People would be responsible to God for what God has already revealed to them (I give you ClubDirt, can see God, but doesn't know him by name). This island scenario fits the explanation for the minority of the worlds population that have down syndrone, isolated tribal community e.c.t. Though KittyKatz, since a non-eternal universe implied that it must have been caused. Maybe Genesis 1:1 is correct. Not to be dismayed by the facts, you have invented some metaphysical "science" that attempts to explain away the existence of God. Hence, most atheistic cosmologists believe that we see only the visible part of a much larger multiverse that randomly spews out universes with different physical parameters. Since there is no evidence supporting this idea (nor can there be, according to the laws of the universe), it is really just a substitute "god" for atheists. And, since this "god" is non-intelligent by definition, it requires a complex hypothesis, which would be ruled out if we use your Occam's razor, which states that one should use the simplest logical explanation for any phenomenon. Purposeful intelligent design of the universe makes much more sense, especially based upon what we know about the design of the universe. Looks like I missed rush hour.