I will make some comments, but some of your questions are not easy to answer--especially the ones about why Adam and Eve or why God did something a certain way. All I can do is to make some guesses. But perhaps they will help you.
The Devil did not tempt Adam and Eve to eat of the Tree of Life because it was not prohibited. They would not have sinned if they had eaten of it. Only the Tree of Knowledge was forbidden. It was there as a way of continuing life for them in the garden. God was offering them a paradise on earth and the means by which they could continue to live forever.
As to their interest in the two trees, God specifically told them to stay away from the Tree of Knowledge of Good and Evil (Genesis 2:16-17). The day that they ate of it, they would die. In truth, it was the Tree of Death, but the primary death in context was spiritual death. Spiritually, they did die the day they ate of the fruit. This later lead to spiritual death.
When they ate of the Tree of Knowledge they did so because they were tempted by the devil. Eve was deceived into thinking she was doing some wonderful thing. Very likely, they had not yet gotten to the Tree of Life because they had not been in the garden very long. For four main rivers to flow out of it (Genesis 2:10-14), it must have been a huge garden. They were allowed to explore at their own leisure. As with children (with which they compare in their innocence), it was not the tree that was allowed that was tempting; it was the tree that was prohibited.
I do not think it was dangerous for them to have the Tree of Life available to them before they had sinned. It was there for their using. I think most people assume that one bite of the fruit from the tree of life would have given them eternal life without another taste. I am not so sure. I think it might have required periodic returns to the fruit in order to continue to live forever. The tree of life in the New Jerusalem has leaves "for the healing of the nations" (Revelation 22:2). I picture the body beginning to wear out a bit as things do in the natural world and then a trip to the tree of life would bring the person back to their original health. However, in contrast with modern medicine, the tree of life would continue to work over and over again forever in the life of everyone who came to it. It would not keep them from aging in any way, but would bring them back to a perfect state of health and youth every time it was used.
