Why does the Torah here mention the name of the Tree, referring to it only as "the Tree in the middle of the Garden"?
Seforno: Because of its proximity to the Tree of Life - as if to warn Adam that He had placed before him Life and death, and that the choice was his. 1
Does this mean that, had Adam not sinned, he would have lived forever?
Ramban (citing Chazal): Adam was indeed destined to live forever, provided he did not sin. 1
The Ramban rejects outright the explanation of 'Anshei Teva', who say thatbeing formed from natural elements, he would have had to die anyway, only if he would sin, he would die sooner (in similar fashion to other Chayvei Misah in the Torah). People who deny Divine creation say so. Rather, since the Creation was performed by Hashem, so too, is continued existence in His Hands!
How is it that Hashem told Adam that on the day he eats from the Tree he will die, yet he lived nine hundred and thirty years?
Ramban and Targun Yonasan: What Hashem meant was (not he would die on that day, but) that he would be Chayav Misah on that day.
Rashi (in Tehilim 25:6): Hashem said that he would die on that day, and, based on that Pasuk, Hashem's day is equal to a thousand years. In that case, Adam did indeed die on that day, just as Hashem said he would. 1
Riva cites a Midrash which says that Hashem gave to Adam one of His years, and Adam gave 70 to his descendants - "Yemei Shenoseinu Bahem Shiv'im Shanah".
Why is death not listed among the curses give to man due to eating from the tree?
Peninim mi'Shulchan ha'Gra: The nature of Mitzvos is "Asher Ya'aseh ha'Adam va'Chai Bahem." In addition, we are commanded to observe them. The nature of Aveiros is lethal poison. The curses listed below are for transgressing Hashem's command.