Is it church teaching, and in what sense (common teaching, theological opinion, dogma, etc.), that natural death is a result of the Fall/consequence of Original Sin?
It is Church teaching that human death is the result of the Fall/consequence of Original Sin. This should be understood in the following sense:
The death that occurred, immediately and directly, as a result of sin was spiritual death, the separation of the human spirit from God. Man broke his relationship with God through disobedience and rebellion. Thus, God’s spirit went out of man.
The death that occurred, mediately and indirectly, as a result of sin was physical death. Prior to the Fall, man possessed preternatural gifts, including immortality. The life of God in his soul sustained him so that his body did not perish. Nor did it suffer from infirmities, illnesses, disease, etc.
However, what should be understood from this is that the body is naturally subject to death, and that without the sustaining life of God indwelling their souls, due to sin, Adam and Eve became subject to that bodily death.
If so, does that mean if the Fall did not happen, everyone after would be living on Earth forever and ever? Would not the Earth be extremely over populated?
There are a few scenarios we may envision, though doing so is purely speculative. First, Adam and Eve, and their descendants, may have chosen to allow their bodies to age and die according to their nature, as it appears Mary did. Note here that they are not subject to death (such that they would die regardless of their will), but that they would have maintained a mastery over it, only allowing it according to their choice.
Second, after living for some length of time, perhaps fulfilling some unique mission, they would have left the earth to enter heaven at some preordained time, and according to the will of God, as perhaps was the case with Elijah.
Third, it is conceivable that they would have spread out from the earth to explore other planets to tend and keep those, according to their call. It might have been the natural mission of man to bring life to dead planets, to make use of them, and keep them according to God’s will. So, the earth wouldn’t be overpopulated, because man would have spread out into the universe. We have some precedence for supposing that this is at least a possibility when we see, for instance, Jesus, in His glorified body, passing through solid walls, and disappearing from their midst. Moreover, Mary and the Saints, even Saints who are still living on earth, appear to have received special graces that allow for things like bi-location, and receiving our prayers in a virtually eternal manner.
But again, this is all speculation.
